-2x-6=2-4x(x-1)

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Solution for -2x-6=2-4x(x-1) equation:


Simplifying
-2x + -6 = 2 + -4x(x + -1)

Reorder the terms:
-6 + -2x = 2 + -4x(x + -1)

Reorder the terms:
-6 + -2x = 2 + -4x(-1 + x)
-6 + -2x = 2 + (-1 * -4x + x * -4x)
-6 + -2x = 2 + (4x + -4x2)

Solving
-6 + -2x = 2 + 4x + -4x2

Solving for variable 'x'.

Reorder the terms:
-6 + -2 + -2x + -4x + 4x2 = 2 + 4x + -4x2 + -2 + -4x + 4x2

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

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

Reorder the terms:
-8 + -6x + 4x2 = 2 + -2 + 4x + -4x + -4x2 + 4x2

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

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

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

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + -3x + 2x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-4 + -3x + 2x2)' equal to zero and attempt to solve: Simplifying -4 + -3x + 2x2 = 0 Solving -4 + -3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2 + -1.5x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -1.5x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -1.5x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1.5x + x2 = 0 + 2 -1.5x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -1.5x + x2 = 2 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = 2 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 2 + 0.5625 Combine like terms: 2 + 0.5625 = 2.5625 0.5625 + -1.5x + x2 = 2.5625 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 2.5625 Calculate the square root of the right side: 1.600781059 Break this problem into two subproblems by setting (x + -0.75) equal to 1.600781059 and -1.600781059.

Subproblem 1

x + -0.75 = 1.600781059 Simplifying x + -0.75 = 1.600781059 Reorder the terms: -0.75 + x = 1.600781059 Solving -0.75 + x = 1.600781059 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 1.600781059 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 1.600781059 + 0.75 x = 1.600781059 + 0.75 Combine like terms: 1.600781059 + 0.75 = 2.350781059 x = 2.350781059 Simplifying x = 2.350781059

Subproblem 2

x + -0.75 = -1.600781059 Simplifying x + -0.75 = -1.600781059 Reorder the terms: -0.75 + x = -1.600781059 Solving -0.75 + x = -1.600781059 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -1.600781059 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -1.600781059 + 0.75 x = -1.600781059 + 0.75 Combine like terms: -1.600781059 + 0.75 = -0.850781059 x = -0.850781059 Simplifying x = -0.850781059

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.350781059, -0.850781059}

Solution

x = {2.350781059, -0.850781059}

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