0=2x^2+8x-1080

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Solution for 0=2x^2+8x-1080 equation: 


Simplifying
0 = 2x2 + 8x + -1080

Reorder the terms:
0 = -1080 + 8x + 2x2

Solving
0 = -1080 + 8x + 2x2

Solving for variable 'x'.

Combine like terms: 0 + 1080 = 1080
1080 + -8x + -2x2 = -1080 + 8x + 2x2 + 1080 + -8x + -2x2

Reorder the terms:
1080 + -8x + -2x2 = -1080 + 1080 + 8x + -8x + 2x2 + -2x2

Combine like terms: -1080 + 1080 = 0
1080 + -8x + -2x2 = 0 + 8x + -8x + 2x2 + -2x2
1080 + -8x + -2x2 = 8x + -8x + 2x2 + -2x2

Combine like terms: 8x + -8x = 0
1080 + -8x + -2x2 = 0 + 2x2 + -2x2
1080 + -8x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
1080 + -8x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(540 + -4x + -1x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(540 + -4x + -1x2)' equal to zero and attempt to solve:

Simplifying
540 + -4x + -1x2 = 0

Solving
540 + -4x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-540 + 4x + x2 = 0

Move the constant term to the right:

Add '540' to each side of the equation.
-540 + 4x + 540 + x2 = 0 + 540

Reorder the terms:
-540 + 540 + 4x + x2 = 0 + 540

Combine like terms: -540 + 540 = 0
0 + 4x + x2 = 0 + 540
4x + x2 = 0 + 540

Combine like terms: 0 + 540 = 540
4x + x2 = 540

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 540 + 4

Reorder the terms:
4 + 4x + x2 = 540 + 4

Combine like terms: 540 + 4 = 544
4 + 4x + x2 = 544

Factor a perfect square on the left side:
(x + 2)(x + 2) = 544

Calculate the square root of the right side: 23.323807579

Break this problem into two subproblems by setting 
(x + 2) equal to 23.323807579 and -23.323807579.


Subproblem 1
x + 2 = 23.323807579

Simplifying
x + 2 = 23.323807579

Reorder the terms:
2 + x = 23.323807579

Solving
2 + x = 23.323807579

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 23.323807579 + -2

Combine like terms: 2 + -2 = 0
0 + x = 23.323807579 + -2
x = 23.323807579 + -2

Combine like terms: 23.323807579 + -2 = 21.323807579
x = 21.323807579

Simplifying
x = 21.323807579


Subproblem 2
x + 2 = -23.323807579

Simplifying
x + 2 = -23.323807579

Reorder the terms:
2 + x = -23.323807579

Solving
2 + x = -23.323807579

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -23.323807579 + -2

Combine like terms: 2 + -2 = 0
0 + x = -23.323807579 + -2
x = -23.323807579 + -2

Combine like terms: -23.323807579 + -2 = -25.323807579
x = -25.323807579

Simplifying
x = -25.323807579


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {21.323807579, -25.323807579}
Solution
x = {21.323807579, -25.323807579}

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