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Chapter 10: Q 264. (page 1236)

In the following exercises, solve by completing the square.

2x2+2x=4

Short Answer

Expert verified

The solutions arex=1andx=-2.

Step by step solution

01

Given information.

Given equation 2x2+2x=4

02

Make the perfect square.

Divide both sides of the equation by 2.

2x2+2x2=42x2+x=2

Add 14to both sides of the equation.

x2+x+14=2+14x2+x+14=94

Writing it as a binomial square.

x2+2脳x脳12+122=94(x+12)2=94

03

Use the square root property. 

x+12=卤94x+12=卤94x+12=卤32

The two equations arex+12=32andx+12=-32.

04

Solve both equations for x.

x+12=32x=32-12x=1Orx+12=-32x=-32-12x=-2

Therefore, the solutions arex=-2andx=1.

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