Q.460. Solve the given equation.6x+5x-6... [FREE SOLUTION]

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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.460. (page 984)

Solve the given equation.
$6 x + 5 \sqrt{x} - 6 = 0$

Short Answer

Expert verified

The solution is $x = \frac{4}{9}$ .

Step by step solution

Step 1. Given information.

The given equation is $6 x + 5 \sqrt{x} - 6 = 0$ .

Step 2. Simplify the equation.

$\begin{array}{rcl} 6 x + 5 \sqrt{x} - 6 & = & 0 \\ 6 {(\sqrt{x})}^{2} + 5 \sqrt{x} - 6 & = & 0 \\ 6 {(\sqrt{x})}^{2} + 9 \sqrt{x} - 4 \sqrt{x} - 6 & = & 0 \\ 3 \sqrt{x} (2 \sqrt{x} + 3) - 2 (2 \sqrt{x} + 3) & = & 0 \\ (2 \sqrt{x} + 3) (3 \sqrt{x} - 2) & = & 0 \end{array}$

Step 3. Solve the equation for x.

$\begin{array}{rcl} 2 \sqrt{x} + 3 & = & 0 \\ 2 \sqrt{x} & = & - 3 \\ \sqrt{x} & = & - \frac{3}{2} (d i s c a r d, b e c a u s e t h e s q u a r e r o o t o f a n u m b e r c a n' t b e n e g a t i v e) \end{array}$

and,

$\begin{array}{rcl} 3 \sqrt{x} - 2 & = & 0 \\ 3 \sqrt{x} & = & 2 \\ \sqrt{x} & = & \frac{2}{3} (s q u a r i n g b o t h s i d e s) \\ x & = & \frac{4}{9} \end{array}$

Step 4. Simplified answer.

Hence, the required solution is $x = \frac{4}{9}$ .

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91影视

Solve the given equation.
$6 x + 5 \sqrt{x} - 6 = 0$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplify the equation.

Step 3. Solve the equation for x.

Step 4. Simplified answer.

One App. One Place for Learning.

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91影视

Solve the given equation.6x+5x-6=0

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplify the equation.

Step 3. Solve the equation for x.

Step 4. Simplified answer.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Decision Maths

Applied Mathematics

Geometry

Statistics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Solve the given equation.
$6 x + 5 \sqrt{x} - 6 = 0$