x(2x-15)=180

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Solution for x(2x-15)=180 equation:


Simplifying
x(2x + -15) = 180

Reorder the terms:
x(-15 + 2x) = 180
(-15 * x + 2x * x) = 180
(-15x + 2x2) = 180

Solving
-15x + 2x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + -15x + 2x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + -15x + 2x2 = 0

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

Divide each side by '2'.
-90 + -7.5x + x2 = 0

Move the constant term to the right:

Add '90' to each side of the equation.
-90 + -7.5x + 90 + x2 = 0 + 90

Reorder the terms:
-90 + 90 + -7.5x + x2 = 0 + 90

Combine like terms: -90 + 90 = 0
0 + -7.5x + x2 = 0 + 90
-7.5x + x2 = 0 + 90

Combine like terms: 0 + 90 = 90
-7.5x + x2 = 90

The x term is -7.5x.  Take half its coefficient (-3.75).
Square it (14.0625) and add it to both sides.

Add '14.0625' to each side of the equation.
-7.5x + 14.0625 + x2 = 90 + 14.0625

Reorder the terms:
14.0625 + -7.5x + x2 = 90 + 14.0625

Combine like terms: 90 + 14.0625 = 104.0625
14.0625 + -7.5x + x2 = 104.0625

Factor a perfect square on the left side:
(x + -3.75)(x + -3.75) = 104.0625

Calculate the square root of the right side: 10.201102882

Break this problem into two subproblems by setting 
(x + -3.75) equal to 10.201102882 and -10.201102882.

Subproblem 1

x + -3.75 = 10.201102882 Simplifying x + -3.75 = 10.201102882 Reorder the terms: -3.75 + x = 10.201102882 Solving -3.75 + x = 10.201102882 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = 10.201102882 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = 10.201102882 + 3.75 x = 10.201102882 + 3.75 Combine like terms: 10.201102882 + 3.75 = 13.951102882 x = 13.951102882 Simplifying x = 13.951102882

Subproblem 2

x + -3.75 = -10.201102882 Simplifying x + -3.75 = -10.201102882 Reorder the terms: -3.75 + x = -10.201102882 Solving -3.75 + x = -10.201102882 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = -10.201102882 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = -10.201102882 + 3.75 x = -10.201102882 + 3.75 Combine like terms: -10.201102882 + 3.75 = -6.451102882 x = -6.451102882 Simplifying x = -6.451102882

Solution

The solution to the problem is based on the solutions from the subproblems. x = {13.951102882, -6.451102882}

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