# To find the real solutions of equation ( x + 2 ) 2 = ( x − 4 ) 2 .

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 1, Problem 68RE
To determine

## To find the real solutions of equation (x+2)2=(x−4)2 .

Expert Solution

The solution is x=1 .

### Explanation of Solution

Given information:

(x+2)2=(x4)2

Formula used:

We will solve equation by changing it to an equivalent equation.

Perfect Square:- (a+b)2=a2+2ab+b2

Perfect Square:- (ab)2=a22ab+b2

Calculations:

=x2+4x+4=x28x+16

=x2+4x+4x2+8x16=0 (Re-writing equation)

=x2x2+4x+8x+416=0 (Combining like terms)

=12x12=0

=12x12+12=0+12 (Adding 12 on both the sides)

=12x=12

=12x12=1212 (Dividing 12 on both the sides)

=x=1

The solution of the equation is x=1 .

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