Solve Using the Square Root Property (x-2)^2=25

Problem

(x−2)2=25

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)=±√(,25)

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

x−2=±5

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

x=2±5

4. Evaluate the two resulting linear equations to find the individual solutions.

x=2+5⇒x=7

x=2−5⇒x=−3

Final Answer

(x−2)2=25⇒x=7,−3

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