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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 9: Q. 9.63 (page 903)

Solve :- $x - 7 \sqrt{x} + 12 = 0$

Short Answer

Expert verified

Solution for equation will be -

$x = 16$
$x = 9$

Step by step solution

01

Step 1. Given Data

Quadratic Equation - $x - 7 \sqrt{x} + 12 = 0$

02

Step 2. To Find

We have to solve it and find the value of x.

03

Step 3. Explanation

Let the value of $\sqrt{x} = u$

Then the equation is -

$x - 7 \sqrt{x} + 12 = 0$

${(\sqrt{x})}^{2} - 7 \sqrt{x} + 12 = 0$

Put the value of $\sqrt{x} = u$

$u^{2} - 7 u + 12 = 0$

$(u - 4) (u - 3) = 0$

By using zero product property -

$u - 4 = 0$ , $u - 3 = 0$

$u = 4$ , $u = 3$

04

Step 4. Calculation

Replace u with $\sqrt{x}$

$\sqrt{x} = 4$ , $\sqrt{x} = 3$

Do square both side -

${(\sqrt{x})}^{2} = 4^{2}$ , ${(\sqrt{x})}^{2} = 3^{2}$

$x = 16$ , $x = 9$

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Most popular questions from this chapter

Solve by using the Quadratic Formula: $25 t^{2} - 40 t = - 16$

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