2x^2+20x-144=0

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Solution for 2x^2+20x-144=0 equation: 


Simplifying
2x2 + 20x + -144 = 0

Reorder the terms:
-144 + 20x + 2x2 = 0

Solving
-144 + 20x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-72 + 10x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-72 + 10x + x2)' equal to zero and attempt to solve:

Simplifying
-72 + 10x + x2 = 0

Solving
-72 + 10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '72' to each side of the equation.
-72 + 10x + 72 + x2 = 0 + 72

Reorder the terms:
-72 + 72 + 10x + x2 = 0 + 72

Combine like terms: -72 + 72 = 0
0 + 10x + x2 = 0 + 72
10x + x2 = 0 + 72

Combine like terms: 0 + 72 = 72
10x + x2 = 72

The x term is 10x.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10x + 25 + x2 = 72 + 25

Reorder the terms:
25 + 10x + x2 = 72 + 25

Combine like terms: 72 + 25 = 97
25 + 10x + x2 = 97

Factor a perfect square on the left side:
(x + 5)(x + 5) = 97

Calculate the square root of the right side: 9.848857802

Break this problem into two subproblems by setting 
(x + 5) equal to 9.848857802 and -9.848857802.


Subproblem 1
x + 5 = 9.848857802

Simplifying
x + 5 = 9.848857802

Reorder the terms:
5 + x = 9.848857802

Solving
5 + x = 9.848857802

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = 9.848857802 + -5

Combine like terms: 5 + -5 = 0
0 + x = 9.848857802 + -5
x = 9.848857802 + -5

Combine like terms: 9.848857802 + -5 = 4.848857802
x = 4.848857802

Simplifying
x = 4.848857802


Subproblem 2
x + 5 = -9.848857802

Simplifying
x + 5 = -9.848857802

Reorder the terms:
5 + x = -9.848857802

Solving
5 + x = -9.848857802

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = -9.848857802 + -5

Combine like terms: 5 + -5 = 0
0 + x = -9.848857802 + -5
x = -9.848857802 + -5

Combine like terms: -9.848857802 + -5 = -14.848857802
x = -14.848857802

Simplifying
x = -14.848857802


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.848857802, -14.848857802}
Solution
x = {4.848857802, -14.848857802}

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