Solve for x (2x-1)^2=18

Problem

(2*x−1)2=18

Solution

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

√(,(2*x−1)2)=±√(,18)

2. Simplify the radical by factoring 18 into 9×2 and taking the square root of the perfect square.

2*x−1=±3√(,2)

3. Isolate the term with x by adding 1 to both sides of the equation.

2*x=1±3√(,2)

4. Solve for x by dividing both sides by 2

x=(1±3√(,2))/2

Final Answer

(2*x−1)2=18⇒x=(1±3√(,2))/2

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