Question

Solve the equations.
a. (x − 2)^2 = 9
b. 3(x − 2)^2 = 9
c. 6 = 24(x + 1)^2

Answer 1

Answer: a) x = 5 or -1 b) x = √3+2

c) x = -1/2 or -3/2

Explanation:

a) (x − 2)² = 9

First step is to take the square root of both sides to eliminate the square

√ (x − 2)² = √9

x-2 = +-3

x = +3+2

x = 5 and;

x = -3+2

x = -1

x = 5 or -1

b) 3(x-2)² = 9

First we divide both sides by 3 to get;

(x-2)² = 9/3

(x-2)² = 3

Second step is to take the square root of both sides to eliminate the square

√(x-2)² = √3

x-2 = √3

x = √3+2

c) 6 = 24(x+1)²

Dividing both sides by 24, we have

6/24 = (x+1)²

1/4 = (x+1)²

Taking the square root of both sides we have

√1/4 = √(x+1)²

= +-1/2 = x+1

x = +1/2-1 = -1/2 and;

x = -1/2-1 = -3/2

x = -1/2 or -3/2