(2x)(x-2)=50

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Solution for (2x)(x-2)=50 equation:


Simplifying
(2x)(x + -2) = 50

Remove parenthesis around (2x)
2x(x + -2) = 50

Reorder the terms:
2x(-2 + x) = 50
(-2 * 2x + x * 2x) = 50
(-4x + 2x2) = 50

Solving
-4x + 2x2 = 50

Solving for variable 'x'.

Reorder the terms:
-50 + -4x + 2x2 = 50 + -50

Combine like terms: 50 + -50 = 0
-50 + -4x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-25 + -2x + x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-25 + -2x + x2)' equal to zero and attempt to solve: Simplifying -25 + -2x + x2 = 0 Solving -25 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + -2x + 25 + x2 = 0 + 25 Reorder the terms: -25 + 25 + -2x + x2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -2x + x2 = 0 + 25 -2x + x2 = 0 + 25 Combine like terms: 0 + 25 = 25 -2x + x2 = 25 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 = 25 + 1 Reorder the terms: 1 + -2x + x2 = 25 + 1 Combine like terms: 25 + 1 = 26 1 + -2x + x2 = 26 Factor a perfect square on the left side: (x + -1)(x + -1) = 26 Calculate the square root of the right side: 5.099019514 Break this problem into two subproblems by setting (x + -1) equal to 5.099019514 and -5.099019514.

Subproblem 1

x + -1 = 5.099019514 Simplifying x + -1 = 5.099019514 Reorder the terms: -1 + x = 5.099019514 Solving -1 + x = 5.099019514 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 = 5.099019514 + 1 Combine like terms: -1 + 1 = 0 0 + x = 5.099019514 + 1 x = 5.099019514 + 1 Combine like terms: 5.099019514 + 1 = 6.099019514 x = 6.099019514 Simplifying x = 6.099019514

Subproblem 2

x + -1 = -5.099019514 Simplifying x + -1 = -5.099019514 Reorder the terms: -1 + x = -5.099019514 Solving -1 + x = -5.099019514 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 = -5.099019514 + 1 Combine like terms: -1 + 1 = 0 0 + x = -5.099019514 + 1 x = -5.099019514 + 1 Combine like terms: -5.099019514 + 1 = -4.099019514 x = -4.099019514 Simplifying x = -4.099019514

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.099019514, -4.099019514}

Solution

x = {6.099019514, -4.099019514}

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