Question

How would you solve a radical equation?

Answer 1

First square both sides to get rid of the square root:
x+7=(x+1)^2
Then use FOIL to solve the right side since it is really (x+1)(x+1)
x+7=x^2+2x+2
Then set it equal to 0
0=x^2+x-5
Factor
(x+3)(x-2)
Set each answer equal to 0
x+3=0
x-2=0
Solve for x
So your answers are x=-3 and x=2

Answer 2

√(x+7) = x + 1
Squaring on both sides,
x + 7 = (x + 1)²
x + 7 = x² + 2x + 1
x² + x - 6 = 0
x² + 3x - 2x - 6 = 0
x(x + 3) - 2(x + 3) = 0
(x - 2)(x + 3) = 0

x = 2 or -3

Hope this helps!