Solve by Factoring (2x-1)^2=8

Problem

(2*x−1)2=8

Solution

1. Expand the squared binomial on the left side of the equation using the identity (a−b)2=a2−2*a*b+b2

4*x2−4*x+1=8

2. Rearrange the equation into standard quadratic form a*x2+b*x+c=0 by subtracting 8 from both sides.

4*x2−4*x−7=0

3. Analyze the quadratic for factoring. Since the quadratic 4*x2−4*x−7 does not have integer factors, we use the quadratic formula x=(−b±√(,b2−4*a*c))/(2*a) to find the roots that would lead to the factors.

x=(−(−4)±√(,(−4)2−4*(4)*(−7)))/(2*(4))

4. Simplify the expression under the radical and the denominator.

x=(4±√(,16+112))/8

x=(4±√(,128))/8

5. Simplify the square root by factoring out the largest perfect square, which is 64.

x=(4±8√(,2))/8

6. Divide each term in the numerator by the denominator to find the final values for x

x=(1±2√(,2))/2

Final Answer

(2*x−1)2=8⇒x=(1±2√(,2))/2

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