Question

Solve. (x + 2)^2 = 1

Answer 1

(x+2)^(2)=1

Take the square root of each side of the equation to setup the solution for x.
~((x+2)^(2))=\~(1)

Remove the perfect root factor (x+2) under the radical to solve for x.
(x+2)=\~(1)

Pull all perfect square roots out from under the radical. In this case, remove the 1 because it is a perfect square.
(x+2)=\1

First, substitute in the + portion of the \ to find the first solution.
(x+2)=1

Remove the parentheses around the expression x+2.
x+2=1

Since 2 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 2 from both sides.
x=-2+1

Add 1 to -2 to get -1.
x=-1

Next, substitute in the - portion of the \ to find the second solution.
(x+2)=-1

Remove the parentheses around the expression x+2.
x+2=-1

Since 2 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 2 from both sides.
x=-2-1

Subtract 1 from -2 to get -3.
x=-3

The complete solution is the result of both the + and - portions of the solution.
x=-1,-3