Solve Using the Square Root Property (x-3)^2=16

Problem

(x−3)2=16

Solution

1. Apply the square root property by taking the square root of both sides of the equation, remembering to include both the positive and negative roots.

√(,(x−3)2)=±√(,16)

2. Simplify the square roots on both sides.

x−3=±4

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

x=3±4

4. Evaluate the two separate cases to find the specific values for x

x=3+4⇒x=7

x=3−4⇒x=−1

Final Answer

(x−3)2=16⇒x=7,−1

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