Solve Using the Square Root Property (x-2)^2=16

Problem

(x−2)2=16

Solution

1. Apply the square root property by taking the square root of both sides of the equation to eliminate the exponent.

√(,(x−2)2)=±√(,16)

2. Simplify the square roots on both sides, remembering to include the plus-minus sign for the constant.

x−2=±4

3. Isolate the variable by adding 2 to both sides of the equation.

x=2±4

4. Solve for both cases to find the two possible values for x

x=2+4⇒x=6

x=2−4⇒x=−2

Final Answer

(x−2)2=16⇒x=6,−2

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