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## Algebra Practice Test

Test your knowledge of introductory Algebra with this Algebra practice exam. Whether you are studying for a school math test or looking to test your math skills, this free practice test will challenge your knowledge of algebra.

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## Algebra Quiz

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## Solving Equations

9th -  10th  , solving systems of equations, 9th -  12th  , systems of equations, one step equations, 11.3k plays.

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## Completing the Square

" Completing the Square " is where we ...

But if you have time, let me show you how to " Complete the Square " yourself.

Say we have a simple expression like x 2 + bx . Having x twice in the same expression can make life hard. What can we do?

Well, with a little inspiration from Geometry we can convert it, like this:

As you can see x 2 + bx can be rearranged nearly into a square ...

... and we can complete the square with (b/2) 2

In Algebra it looks like this:

So, by adding (b/2) 2 we can complete the square.

The result of (x+b/2) 2 has x only once , which is easier to use.

## Keeping the Balance

Now ... we can't just add (b/2) 2 without also subtracting it too! Otherwise the whole value changes.

So let's see how to do it properly with an example:

The result:

x 2 + 6x + 7   =   (x+3) 2 − 2

And now x only appears once, and our job is done!

## A Shortcut Approach

Here is a quick way to get an answer. You may like this method.

First think about the result we want: (x+d) 2 + e

After expanding (x+d) 2 we get: x 2 + 2dx + d 2 + e

Now see if we can turn our example into that form to discover d and e

## Example: try to fit x 2 + 6x + 7 into x 2 + 2dx + d 2 + e

Now we can "force" an answer:

And we get the same result (x+3) 2 − 2 as above!

Now, let us look at a useful application: solving Quadratic Equations ...

## Solving General Quadratic Equations by Completing the Square

We can complete the square to solve a Quadratic Equation (find where it is equal to zero).

But a general Quadratic Equation can have a coefficient of a in front of x 2 :

ax 2 + bx + c = 0

But that is easy to deal with ... just divide the whole equation by "a" first, then carry on:

x 2 + (b/a)x + c/a = 0

Now we can solve a Quadratic Equation in 5 steps:

We now have something that looks like (x + p) 2 = q, which can be solved rather easily:

OK, some examples will help!

## Example 1: Solve x 2 + 4x + 1 = 0

Step 1 can be skipped in this example since the coefficient of x 2 is 1

Step 2 Move the number term to the right side of the equation:

Step 3 Complete the square on the left side of the equation and balance this by adding the same number to the right side of the equation.

(b/2) 2 = (4/2) 2 = 2 2 = 4

Step 4 Take the square root on both sides of the equation:

Step 5 Subtract 2 from both sides:

## Example 2: Solve 5x 2 – 4x – 2 = 0

Step 1 Divide all terms by 5

Step 3 Complete the square on the left side of the equation and balance this by adding the same number to the right side of the equation:

(b/2) 2 = (0.8/2) 2 = 0.4 2 = 0.16

Step 5 Subtract (-0.4) from both sides (in other words, add 0.4):

## Why "Complete the Square"?

Why complete the square when we can just use the Quadratic Formula to solve a Quadratic Equation?

Well, one reason is given above, where the new form not only shows us the vertex, but makes it easier to solve.

There are also times when the form ax 2 + bx + c may be part of a larger question and rearranging it as a(x+ d ) 2 + e makes the solution easier, because x only appears once.

For example "x" may itself be a function (like cos(z) ) and rearranging it may open up a path to a better solution.

Also Completing the Square is the first step in the Derivation of the Quadratic Formula

Just think of it as another tool in your mathematics toolbox.

## Footnote: Values of "d" and "e"

How did I get the values of d and e from the top of the page?

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## Equation Basics Worksheet

Solve each equation.

Click “Show Answer” underneath the problem to see the answer. Or click the “Show Answers” button at the bottom of the page to see all the answers at once.

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## Video transcript

#### IMAGES

1. Solving For Specific Variable Worksheet : 1 : Solve for two unknown

2. Solving For Specific Variable Worksheet / Worksheets With Answers

3. 8 6 Solving Rational Equations Worksheet Form G prentice hall algebra 2

4. Solving Equations Algebra 1 Worksheet Printable

6. Free Worksheets For Linear Equations (Grades 6-9, Pre-Algebra

#### VIDEO

1. Equation Solving Ⅰ Nice Algebra Question Ⅰ You Should Learn This Trick

2. Group 05, Topic 3. Solving Algebraic Equations Using Graphs HES 6 A

3. MTH401

4. GRE Math

5. Equation Solving

6. A look at algebra equations which have extraneous solutions or domain restrictions

1. Solving equations & inequalities

Quiz 1: 5 questions Practice what you've learned, and level up on the above skills Analyzing the number of solutions to linear equations Linear equations with unknown coefficients Quiz 2: 5 questions Practice what you've learned, and level up on the above skills Multi-step inequalities Compound inequalities

2. Algebra (all content)

Solving exponential equations using properties of exponents Introduction to rate of exponential growth and decay Interpreting the rate of change of exponential models (Algebra 2 level) Constructing exponential models according to rate of change (Algebra 2 level) Advanced interpretation of exponential models (Algebra 2 level) Distinguishing betwe...

3. Quiz: Solving Simple Equations

Study Guides Basic Math & Pre-Algebra Quiz: Solving Simple Equations Preliminaries Multiplying and Dividing Using Zero Common Math Symbols Quiz: Ways to Show Multiplication and Division, Multiplying and Dividing by Zero, and Common Math Symbols Properties of Basic Mathematical Operations Quiz: Properties of Basic Mathematical Operations

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2023 Edition Algebra Practice Test Test your knowledge of introductory Algebra with this Algebra practice exam. Whether you are studying for a school math test or looking to test your math skills, this free practice test will challenge your knowledge of algebra. View Answers as You Go View 1 Question at a Time Bookmark Page

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Unit 1: Algebra foundations 0/700 Mastery points Overview and history of algebra Introduction to variables Substitution and evaluating expressions Combining like terms Introduction to equivalent expressions Division by zero Unit 2: Solving equations & inequalities 0/1100 Mastery points

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Course Try it risk-free for 30 days Instructions: Choose an answer and hit 'next'. You will receive your score and answers at the end. question 1 of 3 In the equation 5x - 7 = 8, which number is...

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Linear Equations. 5 problems similar to: 5 = 2x +3. Quadratic Equations. 5 problems similar to: x2 − 3x = 28. Inequalities. 5 problems similar to: 3x+4 > 6.

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Algebra Quiz: Test your algebra skills by answering questions. This quiz asks you to solve algebraic linear and quadratic equations of one variable. Choose difficulty level, question types, and time limit. Algebra Quiz is one of the Interactivate assessment quizzes. On a mission to transform learning through computational thinking, Shodor is ...

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Free student math practice. Change answer; Math

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Free math problem solver answers your algebra homework questions with step-by-step explanations.

11. Algebra

3 Grade 3 3.75 / Solve for the Variable with Addition and Subtraction 3.76 / Solve for the Variable with Multiplication and Division 3.77 / Write Variable Equations to Represent 4 Grade 4 4.94 / Write Variable Expressions 4.95 / Write Variable Equations to Represent 4.96 / Find Two Numbers Based on the Sum and the Difference 4.97 /

12. Quiz

Preview this quiz on Quizizz. quiz for 8th grade students. Find other quizzes for and more on Quizizz for free! ... Algebraic equations Mathematics. 64% accuracy. 1.4K . plays ... Write and solve a subtraction equation to find out how much money Ted took to the aquarium. m - 12 = 5. m - 5 = 12. m + 5 = 12. m + 12 = 5. 14. Multiple-choice. 30 ...

13. Completing the Square

Step 1 Divide all terms by a (the coefficient of x 2).; Step 2 Move the number term (c/a) to the right side of the equation.; Step 3 Complete the square on the left side of the equation and balance this by adding the same value to the right side of the equation.; We now have something that looks like (x + p) 2 = q, which can be solved rather easily: Step 4 Take the square root on both sides of ...

14. Two-step equations

Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. ... Same thing to both sides of equations. Intro to two-step equations. Two-step equations intuition. Worked example: two-step equations. Two-step equations. Math > 7th grade >

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16. Solving Equations Practice Questions

The Corbettmaths Practice Questions on Solving Equations. Videos, worksheets, 5-a-day and much more

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Online practice problems for math, including arithmetic, algebra, calculus, linear algebra, number theory, and statistics. Get help from hints and Step-by-step solutions. Generate printable worksheets.

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In algebra, a quadratic equation (from Latin quadratus 'square') is any equation that can be rearranged in standard form as where x represents an unknown value, and a, b, and c represent known numbers, where a ≠ 0. (If a = 0 and b ≠ 0 then the equation is linear, not quadratic.) The numbers a, b, and c are the coefficients of the equation ...

21. Systems of equations with substitution: -3x-4y=-2 & y=2x-5

This type of equation creates a line where each point on the line represents an (x, y) ordered pair that is a solution to the equation. When you have 2 equations with the same 2 variables, then you have a system of linear equations. The solution to the system is the point (or points) that the 2 linear equations have in common. Hope this helps.