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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 6: Q. 301 (page 627)

In the following exercises, solve:
$20 x^{2} - 60 x = - 45$

Short Answer

Expert verified

On solving the equation, we get $x = \frac{3}{2}$ .

Step by step solution

01

Step 1. Given information.

Consider the given equation,

$20 x^{2} - 60 x = - 45$

Write the quadratic equation in standard form,

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

02

Step 2. Factor the quadratic expression.

On factoring, we get,

$5 (4 x^{2} - 12 x + 9) = 0 4 x^{2} - 6 x - 6 x + 9 = 0 2 x (2 x - 3) - 3 (2 x - 3) = 0 {(2 x - 3)}^{2} = 0$

Use the zero product property,

$2 x - 3 = 0 x = \frac{3}{2}$

03

Step 3. Check the answers.

Substitute $x = \frac{3}{2}$ in the given equation,

$20 {(\frac{3}{2})}^{2} - 60 (\frac{3}{2}) = - 45 20 脳 \frac{9}{4} - 90 = - 45 45 - 90 = - 45 - 45 = - 45$

This is true.

Hence, the answer is $x = \frac{3}{2}$ .

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