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Chapter 10: Q 87 (page 1181)

Solve the equation by completing square method.

(x+6)(x-2)=9

Short Answer

Expert verified

The solutions arex=-7,x=3.

Step by step solution

01

Given Information     

The Given equation is (x+6)(x-2)=9.

02

Multiply the binomials on left.

x2+4x-12=9

Isolate the variables.

x2+4x=9+12

x2+4x=21

Here, b=4.

So,

=b22=422=(2)2 =4

Add 4both sides.

x2+4x+4=21+4x2+4x+4=25

03

Factor the perfect square trinomial as a binomial square.  

(x+2)2=25

Use the square root property.

x+2=卤25x+2=卤5x=-2卤5

Rewrite to show two solutions.

x=-2+5=3x=-2-5=-7

Therefore,x=-7,x=3

04

Check the solutions.

Substitute x=-7

(x+6)(x-2)=9(-7+6)(-7-2)=?9(-1)(-9)=?99=9True

Substitute x=3

(x+6)(x-2)=9(3+6)(3-2)=?9(9)(1)=?99=9True

Thus, the solutions arex=-7,x=3.

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