(2x^2+12x-180)-2x=0

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Solution for (2x^2+12x-180)-2x=0 equation:


Simplifying
(2x2 + 12x + -180) + -2x = 0

Reorder the terms:
(-180 + 12x + 2x2) + -2x = 0

Remove parenthesis around (-180 + 12x + 2x2)
-180 + 12x + 2x2 + -2x = 0

Reorder the terms:
-180 + 12x + -2x + 2x2 = 0

Combine like terms: 12x + -2x = 10x
-180 + 10x + 2x2 = 0

Solving
-180 + 10x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-90 + 5x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-90 + 5x + x2)' equal to zero and attempt to solve:

Simplifying
-90 + 5x + x2 = 0

Solving
-90 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '90' to each side of the equation.
-90 + 5x + 90 + x2 = 0 + 90

Reorder the terms:
-90 + 90 + 5x + x2 = 0 + 90

Combine like terms: -90 + 90 = 0
0 + 5x + x2 = 0 + 90
5x + x2 = 0 + 90

Combine like terms: 0 + 90 = 90
5x + x2 = 90

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 90 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 90 + 6.25

Combine like terms: 90 + 6.25 = 96.25
6.25 + 5x + x2 = 96.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 96.25

Calculate the square root of the right side: 9.810708435

Break this problem into two subproblems by setting 
(x + 2.5) equal to 9.810708435 and -9.810708435.


Subproblem 1
x + 2.5 = 9.810708435

Simplifying
x + 2.5 = 9.810708435

Reorder the terms:
2.5 + x = 9.810708435

Solving
2.5 + x = 9.810708435

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 9.810708435 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 9.810708435 + -2.5
x = 9.810708435 + -2.5

Combine like terms: 9.810708435 + -2.5 = 7.310708435
x = 7.310708435

Simplifying
x = 7.310708435


Subproblem 2
x + 2.5 = -9.810708435

Simplifying
x + 2.5 = -9.810708435

Reorder the terms:
2.5 + x = -9.810708435

Solving
2.5 + x = -9.810708435

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -9.810708435 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -9.810708435 + -2.5
x = -9.810708435 + -2.5

Combine like terms: -9.810708435 + -2.5 = -12.310708435
x = -12.310708435

Simplifying
x = -12.310708435


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.310708435, -12.310708435}
Solution
x = {7.310708435, -12.310708435}

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