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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 7: Q. 341 (page 893)

Solve Quadratic Equations by Factoring
In the following exercises, solve.
$20 x^{2} - 60 x = - 45$

Short Answer

Expert verified

The solution is $x = \frac{3}{2}, \frac{3}{2}$ .

Step by step solution

01

Step 1. Given Information

We are given the quadratic equation $20 x^{2} - 60 x = - 45$ and we need to solve it by factoring.

02

Step 2. Solving the quadratic

Writing the quadratic equation in standard form:

$20 x^{2} - 60 x = - 45 鈬� 20 x^{2} - 60 x + 45 = 0$

Factoring the quadratic we get,

role="math" localid="1647795925993" $20 x^{2} - 60 x + 45 = 0 鈬� 5 (4 x^{2} - 12 x + 9) = 0 鈬� (4 x^{2} - 12 x + 9) = 0 鈬� {(2 x)}^{2} - 2 脳 2 x 脳 3 + {(3)}^{2} = 0 鈬� {(2 x - 3)}^{2} = 0$

Use the Zero Product Property to set each factor to ,

${(2 x - 3)}^{2} = 0 鈬� (2 x - 3) = 0 鈬� 2 x = 3 鈬� x = \frac{3}{2} 鈭� x = \frac{3}{2}, \frac{3}{2}$

03

Step 3. Checking the answers

Substituting each solution separately into the original equation:

$x = \frac{3}{2}, 20 x^{2} - 60 x = - 45 鈬� 20 {(\frac{3}{2})}^{2} - 60 (\frac{3}{2}) = - 45 鈬� 20 脳 \frac{9}{4} - 60 脳 \frac{3}{2} = - 45 鈬� 5 脳 9 - 30 脳 3 = - 45 鈬� 45 - 90 = - 45 鈬� - 45 = - 45$

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