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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 9: Q.459. (page 984)

Solve the given equation.
$x + 3 \sqrt{x} - 28 = 0$

Short Answer

Expert verified

The solution is $x = 16$ .

Step by step solution

01

Step 1. Given information.

The given equation is $x + 3 \sqrt{x} - 28 = 0$ .

02

Step 2. Simplify the given equation.

$\begin{array}{rcl} x + 3 \sqrt{x} - 28 & = & 0 \\ {(\sqrt{x})}^{2} + 3 \sqrt{x} - 28 & = & 0 \\ {(\sqrt{x})}^{2} + 7 \sqrt{x} - 4 \sqrt{x} - 28 & = & 0 \\ \sqrt{x} (\sqrt{x} + 7) - 4 (\sqrt{x} + 7) & = & 0 \\ (\sqrt{x} + 7) (\sqrt{x} - 4) & = & 0 \end{array}$

03

Step 3. Solve the equation for x.

$\begin{array}{rcl} \sqrt{x} + 7 & = & 0 \\ \sqrt{x} & = & - 7 (r e j e c t e d, s q u a r e r o o t o f a n u m b e r c a n' t b e n e g a t i v e) \end{array}$

and,

$\begin{array}{rcl} \sqrt{x} - 4 & = & 0 \\ \sqrt{x} & = & 4 鈰� 鈰� (s q u a r i n g b o t h s i d e s) \\ x & = & 16 \end{array}$

04

Step 4. Simplified answer.

Hence, the required solution is $x = 16$ .

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