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Chapter 10: Q 248 (page 1236)

In the following exercises, solve by completing the square.

d2+14d=-13

Short Answer

Expert verified

The solutions ared=-1andd=-13.

Step by step solution

01

Given information

The given equation isd2+14d=-13

02

Make the perfect square.

Adding 49 to both sides of the equation.

d2+14d+49=-13+49d2+14d+49=36

Writing it as a binomial square.

d2+2脳d脳7+72=36(d+7)2=36d2+2脳d脳7+72=36(d+7)2=36

03

Use the square root property. 

d+7=卤36d+7=卤62d+7=卤6

The two equations arelocalid="1657725370893" d+7=6andd+7=-6.

04

Solve both equations for d.

d+7=+6d=6-7d=-1Ord+7=-6d=-6-7d=-13

Therefore, the two solutions are=-13andd=-1.

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