Solve the equation for real solutions by using the square root property.

(x+1)^2=64

1 answer

To solve the equation (x+1)^2=64 using the square root property, we will isolate x and take the square root of both sides of the equation.

First, expand the left side of the equation:
(x+1)(x+1) = 64
x^2 + 2x + 1 = 64

Next, subtract 64 from both sides of the equation to isolate the x terms:
x^2 + 2x + 1 - 64 = 0
x^2 + 2x - 63 = 0

Now, we can use the square root property. Take the square root of both sides of the equation to solve for x:

x + 1 = ±√64
x + 1 = ±8

Next, isolate x by subtracting 1 from both sides of the equation:

x = -1 ± 8

This gives two possible solutions for x:

x = -1 + 8 = 7
x = -1 - 8 = -9

Therefore, the equation (x+1)^2 = 64 has two real solutions, x = 7 and x = -9.