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Updated on Sep 23, 2011

Introduction

This set of practice questions will give you practice in finding solutions to quadratic equations. Quadratic equations are those equations that can be written in the form ax2 + bx + c = 0, where a ≠ 0. While there are several methods for solving quadratic equations, solutions for all the equations presented here can be found by factoring.

In some algebra problems, you practiced factoring polynomials by using the greatest common factor method, the difference of two perfect squares method, and the trinomial factor method. Use these methods to factor the equations that have been transformed into quadratic equations. Then, using the zero product property (if (a)(b) = 0, then a = 0 or b = 0 or both = 0), let each factor equal zero and solve for the variable. There will be two solutions for each quadratic equation. (Ignore numerical factors such as the 3 in the factored equation 3(x + 1)(x + 1) = 0 when finding solutions to quadratic equations. The solutions will be the same for equations with or without the numerical factors.)

Practice Questions

Find the solutions to the following quadratic equations.

1. x2 – 25 = 0
2. n2 – 169 = 0
3. a2 + 12a + 32 = 0
4. y2 – 15y + 56 = 0
5. b2 + b – 90 = 0
6. 4x2 = 49
7. 25r2 = 144
8. 2n2 + 20n + 42 = 0
9. 3c2 – 33c – 78 = 0
10. 100r2 = 144
11. 3x2 – 36x + 108 = 0
12. 7a2 – 21a – 28 = 0
13. 8y2 + 56y + 96 = 0
14. 2x2 + 9x = –10
15. 4x2 + 4x = 15
16. 9x2 + 12x = –4
17. 3x2 = 19x – 20
18. 8b2 + 10b = 42
19. 14n2 = 7n + 21
20. 6b2 + 20b = –9b – 20
21. 15x2 – 70x – 120 = 0
22. 7x2 = 52x – 21
23. 36z2 + 78z = –36
24. 12r2 = 192 – 40r
25. 24x2 = 3(43x – 15)

Numerical expressions in parentheses like this [ ] are operations performed on only part of the original expression. The operations performed within these symbols are intended to show how to evaluate the various terms that make up the entire expression.

Expressions with parentheses that look like this () contain either numerical substitutions or expressions that are part of a numerical expression. Once a single number appears within these parentheses, the parentheses are no longer needed and need not be used the next time the entire expression is written.

When two pair of parentheses appear side by side like this ()(), it means that the expressions within are to be multiplied.

Sometimes parentheses appear within other parentheses in numerical or algebraic expressions. Regardless of what symbol is used, (), { }, or [ ], perform operations in the innermost parentheses first and work outward.

The solutions are underlined.

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