(x+2)(4x-137)=180

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Solution for (x+2)(4x-137)=180 equation:


Simplifying
(x + 2)(4x + -137) = 180

Reorder the terms:
(2 + x)(4x + -137) = 180

Reorder the terms:
(2 + x)(-137 + 4x) = 180

Multiply (2 + x) * (-137 + 4x)
(2(-137 + 4x) + x(-137 + 4x)) = 180
((-137 * 2 + 4x * 2) + x(-137 + 4x)) = 180
((-274 + 8x) + x(-137 + 4x)) = 180
(-274 + 8x + (-137 * x + 4x * x)) = 180
(-274 + 8x + (-137x + 4x2)) = 180

Combine like terms: 8x + -137x = -129x
(-274 + -129x + 4x2) = 180

Solving
-274 + -129x + 4x2 = 180

Solving for variable 'x'.

Reorder the terms:
-274 + -180 + -129x + 4x2 = 180 + -180

Combine like terms: -274 + -180 = -454
-454 + -129x + 4x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-454 + -129x + 4x2 = 0

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
-113.5 + -32.25x + x2 = 0

Move the constant term to the right:

Add '113.5' to each side of the equation.
-113.5 + -32.25x + 113.5 + x2 = 0 + 113.5

Reorder the terms:
-113.5 + 113.5 + -32.25x + x2 = 0 + 113.5

Combine like terms: -113.5 + 113.5 = 0.0
0.0 + -32.25x + x2 = 0 + 113.5
-32.25x + x2 = 0 + 113.5

Combine like terms: 0 + 113.5 = 113.5
-32.25x + x2 = 113.5

The x term is -32.25x.  Take half its coefficient (-16.125).
Square it (260.015625) and add it to both sides.

Add '260.015625' to each side of the equation.
-32.25x + 260.015625 + x2 = 113.5 + 260.015625

Reorder the terms:
260.015625 + -32.25x + x2 = 113.5 + 260.015625

Combine like terms: 113.5 + 260.015625 = 373.515625
260.015625 + -32.25x + x2 = 373.515625

Factor a perfect square on the left side:
(x + -16.125)(x + -16.125) = 373.515625

Calculate the square root of the right side: 19.326552331

Break this problem into two subproblems by setting 
(x + -16.125) equal to 19.326552331 and -19.326552331.

Subproblem 1

x + -16.125 = 19.326552331 Simplifying x + -16.125 = 19.326552331 Reorder the terms: -16.125 + x = 19.326552331 Solving -16.125 + x = 19.326552331 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.125' to each side of the equation. -16.125 + 16.125 + x = 19.326552331 + 16.125 Combine like terms: -16.125 + 16.125 = 0.000 0.000 + x = 19.326552331 + 16.125 x = 19.326552331 + 16.125 Combine like terms: 19.326552331 + 16.125 = 35.451552331 x = 35.451552331 Simplifying x = 35.451552331

Subproblem 2

x + -16.125 = -19.326552331 Simplifying x + -16.125 = -19.326552331 Reorder the terms: -16.125 + x = -19.326552331 Solving -16.125 + x = -19.326552331 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.125' to each side of the equation. -16.125 + 16.125 + x = -19.326552331 + 16.125 Combine like terms: -16.125 + 16.125 = 0.000 0.000 + x = -19.326552331 + 16.125 x = -19.326552331 + 16.125 Combine like terms: -19.326552331 + 16.125 = -3.201552331 x = -3.201552331 Simplifying x = -3.201552331

Solution

The solution to the problem is based on the solutions from the subproblems. x = {35.451552331, -3.201552331}

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