Solve Using the Square Root Property (x-1)^2=9

Problem

(x−1)2=9

Solution

1. Identify the equation as being in the form u2=d where u=x−1 and d=9

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−1)=±√(,9)

3. Simplify the square root of the constant term.

x−1=±3

4. Isolate the variable x by adding 1 to both sides of the equation.

x=1±3

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

x=1+3⇒x=4

x=1−3⇒x=−2

Final Answer

(x−1)2=9⇒x=4,−2

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