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Chapter 10: Q 253. (page 1236)

In the following exercises, solve by completing the square.

v2-14v=-31

Short Answer

Expert verified

The solutions arev=-32+7andv=32+7.

Step by step solution

01

Given information. 

Given equation v2-14v=-31

02

Make the perfect square.

Add 49 to both sides of the equation.

v2-14v+49=-31+49v2-14v+49=18

Writing it as a binomial square.

v2-2脳v脳7+72=18(v-7)2=18

03

Use the square root property. 

v-7=卤18

Simplify the radical.

v-7=卤9脳2v-7=卤9脳2v-7=卤3脳2v-7=卤32

The two equations arev-7=32andv-7=-32.

04

Solve both equations for v.

v-7=-32v=-32+7Orv-7=32v=32+7

Therefore, the solutions arev=32+7andv=-32+7.

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