(2x-2)(2x-2)-6=0

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Solution for (2x-2)(2x-2)-6=0 equation:


Simplifying
(2x + -2)(2x + -2) + -6 = 0

Reorder the terms:
(-2 + 2x)(2x + -2) + -6 = 0

Reorder the terms:
(-2 + 2x)(-2 + 2x) + -6 = 0

Multiply (-2 + 2x) * (-2 + 2x)
(-2(-2 + 2x) + 2x * (-2 + 2x)) + -6 = 0
((-2 * -2 + 2x * -2) + 2x * (-2 + 2x)) + -6 = 0
((4 + -4x) + 2x * (-2 + 2x)) + -6 = 0
(4 + -4x + (-2 * 2x + 2x * 2x)) + -6 = 0
(4 + -4x + (-4x + 4x2)) + -6 = 0

Combine like terms: -4x + -4x = -8x
(4 + -8x + 4x2) + -6 = 0

Reorder the terms:
4 + -6 + -8x + 4x2 = 0

Combine like terms: 4 + -6 = -2
-2 + -8x + 4x2 = 0

Solving
-2 + -8x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + -4x + 2x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-1 + -4x + 2x2)' equal to zero and attempt to solve: Simplifying -1 + -4x + 2x2 = 0 Solving -1 + -4x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.5 + -2x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -2x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -2x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -2x + x2 = 0 + 0.5 -2x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -2x + x2 = 0.5 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 = 0.5 + 1 Reorder the terms: 1 + -2x + x2 = 0.5 + 1 Combine like terms: 0.5 + 1 = 1.5 1 + -2x + x2 = 1.5 Factor a perfect square on the left side: (x + -1)(x + -1) = 1.5 Calculate the square root of the right side: 1.224744871 Break this problem into two subproblems by setting (x + -1) equal to 1.224744871 and -1.224744871.

Subproblem 1

x + -1 = 1.224744871 Simplifying x + -1 = 1.224744871 Reorder the terms: -1 + x = 1.224744871 Solving -1 + x = 1.224744871 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 = 1.224744871 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.224744871 + 1 x = 1.224744871 + 1 Combine like terms: 1.224744871 + 1 = 2.224744871 x = 2.224744871 Simplifying x = 2.224744871

Subproblem 2

x + -1 = -1.224744871 Simplifying x + -1 = -1.224744871 Reorder the terms: -1 + x = -1.224744871 Solving -1 + x = -1.224744871 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 = -1.224744871 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.224744871 + 1 x = -1.224744871 + 1 Combine like terms: -1.224744871 + 1 = -0.224744871 x = -0.224744871 Simplifying x = -0.224744871

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.224744871, -0.224744871}

Solution

x = {2.224744871, -0.224744871}

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