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Chapter 10: Q 74 (page 1181)

Solve the equation by completing square method.

d2-8d=9

Short Answer

Expert verified

The solutions ared=-1,d=9

Step by step solution

01

Given Information.  

The Given equation is d2-8d=9.

02

Isolate the variable terms on one side and the constant terms on the other. 

The variable terms are on the left side.

d2-8d=9

Here,b=-8.

03

Find 12b2and add to the both sides of equation.

=12(-8)2=-42=16

Add 16both sides.

d2-8d+16=9+16d2-8d+16=25

04

Factor the perfect square trinomial as a binomial square. 

(d-4)2=25

Use the square root property.

d-4=卤25d-4=卤5d=4卤5

Rewrite to show two solutions.

d=4卤5d=4+5=9

The solutions ared=-1,d=9

05

Check the solutions. 

Substitute d=-1.

d2-8d=9(-1)2-8(-1)=?91+8=?99=9True

Substitute d=9.

d2-8d=9(9)2-8(9)=?981-72=?99=9True

Thus, the solutions ared=-1,d=9

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