2x^2+8x-560=0

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Solution for 2x^2+8x-560=0 equation: 


Simplifying
2x2 + 8x + -560 = 0

Reorder the terms:
-560 + 8x + 2x2 = 0

Solving
-560 + 8x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-280 + 4x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-280 + 4x + x2)' equal to zero and attempt to solve:

Simplifying
-280 + 4x + x2 = 0

Solving
-280 + 4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '280' to each side of the equation.
-280 + 4x + 280 + x2 = 0 + 280

Reorder the terms:
-280 + 280 + 4x + x2 = 0 + 280

Combine like terms: -280 + 280 = 0
0 + 4x + x2 = 0 + 280
4x + x2 = 0 + 280

Combine like terms: 0 + 280 = 280
4x + x2 = 280

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 = 280 + 4

Reorder the terms:
4 + 4x + x2 = 280 + 4

Combine like terms: 280 + 4 = 284
4 + 4x + x2 = 284

Factor a perfect square on the left side:
(x + 2)(x + 2) = 284

Calculate the square root of the right side: 16.852299546

Break this problem into two subproblems by setting 
(x + 2) equal to 16.852299546 and -16.852299546.


Subproblem 1
x + 2 = 16.852299546

Simplifying
x + 2 = 16.852299546

Reorder the terms:
2 + x = 16.852299546

Solving
2 + x = 16.852299546

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 = 16.852299546 + -2

Combine like terms: 2 + -2 = 0
0 + x = 16.852299546 + -2
x = 16.852299546 + -2

Combine like terms: 16.852299546 + -2 = 14.852299546
x = 14.852299546

Simplifying
x = 14.852299546


Subproblem 2
x + 2 = -16.852299546

Simplifying
x + 2 = -16.852299546

Reorder the terms:
2 + x = -16.852299546

Solving
2 + x = -16.852299546

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 = -16.852299546 + -2

Combine like terms: 2 + -2 = 0
0 + x = -16.852299546 + -2
x = -16.852299546 + -2

Combine like terms: -16.852299546 + -2 = -18.852299546
x = -18.852299546

Simplifying
x = -18.852299546


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.852299546, -18.852299546}
Solution
x = {14.852299546, -18.852299546}

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