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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 6.97 (page 619)

Solve, $8 x^{3} = 24 x^{2} - 18 x$

Short Answer

Expert verified

The value is $x = \frac{3}{2}$

Step by step solution

01

Given information

Given the equation $8 x^{3} = 24 x^{2} - 18 x$

02

Bring all terms to one side and solve

Bringing to one side, we get

$8 x^{3} = 24 x^{2} - 18 x 8 x^{3} - 24 x^{2} + 18 x = 0 x (8 x^{2} - 24 x + 18) = 0$

03

Using the zero factor property calculate the value

Using zero factor property

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

04

Checking the value

Substituting, we get

$8 {(\frac{3}{2})}^{3} = 24 {(\frac{3}{2})}^{2} - 18 (\frac{3}{2}) 8 脳 \frac{27}{8} = 24 脳 \frac{9}{4} - 27 27 = 54 - 27 27 = 27$

So its correct

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Most popular questions from this chapter

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