Chapter 9: Q14. (page 597)

Solve each equation by completing the square.
$2 x^{2} - 36 = - 6 x$

Short Answer

Expert verified

The solutions of the quadratic equation are $- 6$ and 3.

Step by step solution

Step 1. Complete the square.

Complete the square to solve the quadratic equations by isolating $x^{2}$ andbx-terms.

$2 x^{2} - 36 = - 6 x 2 x^{2} + 6 x - 36 = 0 [Standard Form] \frac{2 x^{2} + 6 x - 66}{2} = \frac{0}{2} [Divide by 2] x^{2} + 3 x - 18 = 0 x^{2} + 3 x - 18 + \frac{9}{4} = 0 + \frac{9}{4} [Since {(\frac{3}{2})}^{2} = \frac{9}{4} add to each side] x^{2} + 3 x + \frac{9}{4} - 18 + 18 = \frac{9}{4} + 18 [Add 6 to each side] x^{2} + 3 x + \frac{9}{4} = \frac{81}{4}$

Step 2. Take the square root of each side.

First factor $x^{2} + 3 x + \frac{9}{4}$ , then take square root of each side.

${(x + \frac{3}{2})}^{2} = \frac{81}{4} \sqrt{{(x + \frac{3}{2})}^{2}} = \pm \sqrt{\frac{81}{4}} x + \frac{3}{2} = \pm \frac{9}{2}$

Step 3. Write the solutions.

Subtract $\frac{3}{2}$ from both sides and separate the solutions.

$x + \frac{3}{2} - \frac{3}{2} = - \frac{3}{2} \pm \frac{9}{2} x = - \frac{3}{2} - \frac{9}{2} or x = - \frac{3}{2} + \frac{9}{2} x = - 6 or x = 3$

Therefore, the solutions of the equation are $- 6$ and 3.

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Solve each equation by completing the square.
$2 x^{2} - 36 = - 6 x$

Short Answer

Step by step solution

Step 1. Complete the square.

Step 2. Take the square root of each side.

Step 3. Write the solutions.

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Solve each equation by completing the square.2x2−36=−6x

Short Answer

Step by step solution

Step 1. Complete the square.

Step 2. Take the square root of each side.

Step 3. Write the solutions.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Decision Maths

Logic and Functions

Mechanics Maths

Calculus

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Solve each equation by completing the square.
$2 x^{2} - 36 = - 6 x$