4x(x-2)=2x-2

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


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

Reorder the terms:
4x(-2 + x) = 2x + -2
(-2 * 4x + x * 4x) = 2x + -2
(-8x + 4x2) = 2x + -2

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

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

Solving for variable 'x'.

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

Combine like terms: -8x + -2x = -10x
2 + -10x + 4x2 = -2 + 2x + 2 + -2x

Reorder the terms:
2 + -10x + 4x2 = -2 + 2 + 2x + -2x

Combine like terms: -2 + 2 = 0
2 + -10x + 4x2 = 0 + 2x + -2x
2 + -10x + 4x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
2 + -10x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + -5x + 2x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(1 + -5x + 2x2)' equal to zero and attempt to solve: Simplifying 1 + -5x + 2x2 = 0 Solving 1 + -5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 0.5 + -2.5x + x2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -2.5x + -0.5 + x2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -2.5x + x2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -2.5x + x2 = 0 + -0.5 -2.5x + x2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -2.5x + x2 = -0.5 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = -0.5 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = -0.5 + 1.5625 Combine like terms: -0.5 + 1.5625 = 1.0625 1.5625 + -2.5x + x2 = 1.0625 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 1.0625 Calculate the square root of the right side: 1.030776406 Break this problem into two subproblems by setting (x + -1.25) equal to 1.030776406 and -1.030776406.

Subproblem 1

x + -1.25 = 1.030776406 Simplifying x + -1.25 = 1.030776406 Reorder the terms: -1.25 + x = 1.030776406 Solving -1.25 + x = 1.030776406 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 1.030776406 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 1.030776406 + 1.25 x = 1.030776406 + 1.25 Combine like terms: 1.030776406 + 1.25 = 2.280776406 x = 2.280776406 Simplifying x = 2.280776406

Subproblem 2

x + -1.25 = -1.030776406 Simplifying x + -1.25 = -1.030776406 Reorder the terms: -1.25 + x = -1.030776406 Solving -1.25 + x = -1.030776406 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -1.030776406 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -1.030776406 + 1.25 x = -1.030776406 + 1.25 Combine like terms: -1.030776406 + 1.25 = 0.219223594 x = 0.219223594 Simplifying x = 0.219223594

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.280776406, 0.219223594}

Solution

x = {2.280776406, 0.219223594}

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