(2x-2)(2x-2)=26

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Solution for (2x-2)(2x-2)=26 equation:


Simplifying
(2x + -2)(2x + -2) = 26

Reorder the terms:
(-2 + 2x)(2x + -2) = 26

Reorder the terms:
(-2 + 2x)(-2 + 2x) = 26

Multiply (-2 + 2x) * (-2 + 2x)
(-2(-2 + 2x) + 2x * (-2 + 2x)) = 26
((-2 * -2 + 2x * -2) + 2x * (-2 + 2x)) = 26
((4 + -4x) + 2x * (-2 + 2x)) = 26
(4 + -4x + (-2 * 2x + 2x * 2x)) = 26
(4 + -4x + (-4x + 4x2)) = 26

Combine like terms: -4x + -4x = -8x
(4 + -8x + 4x2) = 26

Solving
4 + -8x + 4x2 = 26

Solving for variable 'x'.

Reorder the terms:
4 + -26 + -8x + 4x2 = 26 + -26

Combine like terms: 4 + -26 = -22
-22 + -8x + 4x2 = 26 + -26

Combine like terms: 26 + -26 = 0
-22 + -8x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-11 + -4x + 2x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-11 + -4x + 2x2)' equal to zero and attempt to solve: Simplifying -11 + -4x + 2x2 = 0 Solving -11 + -4x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -5.5 + -2x + x2 = 0 Move the constant term to the right: Add '5.5' to each side of the equation. -5.5 + -2x + 5.5 + x2 = 0 + 5.5 Reorder the terms: -5.5 + 5.5 + -2x + x2 = 0 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + -2x + x2 = 0 + 5.5 -2x + x2 = 0 + 5.5 Combine like terms: 0 + 5.5 = 5.5 -2x + x2 = 5.5 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 5.5 + 1 Reorder the terms: 1 + -2x + x2 = 5.5 + 1 Combine like terms: 5.5 + 1 = 6.5 1 + -2x + x2 = 6.5 Factor a perfect square on the left side: (x + -1)(x + -1) = 6.5 Calculate the square root of the right side: 2.549509757 Break this problem into two subproblems by setting (x + -1) equal to 2.549509757 and -2.549509757.

Subproblem 1

x + -1 = 2.549509757 Simplifying x + -1 = 2.549509757 Reorder the terms: -1 + x = 2.549509757 Solving -1 + x = 2.549509757 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 2.549509757 + 1 Combine like terms: -1 + 1 = 0 0 + x = 2.549509757 + 1 x = 2.549509757 + 1 Combine like terms: 2.549509757 + 1 = 3.549509757 x = 3.549509757 Simplifying x = 3.549509757

Subproblem 2

x + -1 = -2.549509757 Simplifying x + -1 = -2.549509757 Reorder the terms: -1 + x = -2.549509757 Solving -1 + x = -2.549509757 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -2.549509757 + 1 Combine like terms: -1 + 1 = 0 0 + x = -2.549509757 + 1 x = -2.549509757 + 1 Combine like terms: -2.549509757 + 1 = -1.549509757 x = -1.549509757 Simplifying x = -1.549509757

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.549509757, -1.549509757}

Solution

x = {3.549509757, -1.549509757}

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