Radical Equation An equation that has a variable in the radical.

How to Solve :

How to Solve 1. Isolate the radical.
2. Raise both sides to the appropriate power.
3. Solve the polynomial equation.
4. Check your solutions to make sure they are not extraneous.

Solve :

Solve x = 5
x = 5^2
x = 25 Square both sides to remove the radical over x 3 x = 8
x = 8^3
x = 512 Cube both sides to remove the radical

Solve x+7 = x+1
x+7 = (x+1)^2
x+7 = (x+1) (x+1)
x+7 = x^2 + 2x + 1
-7 -7
x= x^2 + 2x - 6 (x+3) (x-2) = 0
x = -3 and x =2
Check for extraneous solutions
x = -3 x = 2

Solve :

Solve x+2 + 1 = 3–x
Square each side- you must FOIL
x + 2 + 2 x + 2 + 1 = 3 – x
2 x + 2 = -2x
x+2 = -x
x + 2 =x^2 x^2 – x – 2 = 0
(x-2) (x+1)
x = 2 x = -1
Check for extraneous solutions
x = 2 x= -1

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