Solve Using the Square Root Property (x-5)^2=4

Problem

(x−5)2=4

Solution

1. Identify the equation as being in the form u2=d where u=x−5 and d=4

2. Apply the square root property by taking the square root of both sides of the equation and including both positive and negative roots.

(x−5)=±√(,4)

3. Simplify the square root of the constant term.

x−5=±2

4. Isolate the variable x by adding 5 to both sides of the equation.

x=5±2

5. Evaluate the two resulting linear equations to find the specific values for x

x=5+2⇒x=7

x=5−2⇒x=3

Final Answer

(x−5)2=4⇒x=7,3

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