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Chapter 10: Q 69 (page 1181)

Solve the equation by completing square method.

v2+6v=40

Short Answer

Expert verified

The solutions arev=-10,v=4.

Step by step solution

01

Given Information.  

The Given equation isv2+6v=40.

02

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

The variable terms are on the left side.

v2+6v=40

The coefficient of vis 6.

So,b=6

03

Find 12b2and add to the both sides of equation.

=12(6)2=(3)2 =9

Add 9both sides.

v2+6v+9=40+9v2+6v+9=49

04

Factor the perfect square trinomial as a binomial square.

(v+3)2=49

Use the square root property.

v+3=卤49v+3=卤7v=-3卤7

Rewrite to show two solutions.

v=-3+7=4v=-3-7=-10v=-10,v=4

05

Check the solutions.

Substitute v=-10

v2+6v=40(-10)2+6(-10)=?40100-60=?4040=40True

Substitute v=4

v2+6v=40(4)2+6(4)=?4016+24=?4040=40

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