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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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.

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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

Applied Mathematics

Logic and Functions

Calculus

Theoretical and Mathematical Physics

Decision Maths

Mechanics Maths

Study anywhere. Anytime. Across all devices.

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