2x^2+15x-180=0

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Solution for 2x^2+15x-180=0 equation:


Simplifying
2x2 + 15x + -180 = 0

Reorder the terms:
-180 + 15x + 2x2 = 0

Solving
-180 + 15x + 2x2 = 0

Solving for variable 'x'.

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 = 6.451102882 x = 6.451102882 Simplifying x = 6.451102882

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 = -13.951102882 x = -13.951102882 Simplifying x = -13.951102882

Solution

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

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