2x^2+10x-218=0

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Solution for 2x^2+10x-218=0 equation: 


Simplifying
2x2 + 10x + -218 = 0

Reorder the terms:
-218 + 10x + 2x2 = 0

Solving
-218 + 10x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-109 + 5x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-109 + 5x + x2)' equal to zero and attempt to solve:

Simplifying
-109 + 5x + x2 = 0

Solving
-109 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '109' to each side of the equation.
-109 + 5x + 109 + x2 = 0 + 109

Reorder the terms:
-109 + 109 + 5x + x2 = 0 + 109

Combine like terms: -109 + 109 = 0
0 + 5x + x2 = 0 + 109
5x + x2 = 0 + 109

Combine like terms: 0 + 109 = 109
5x + x2 = 109

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 = 109 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 109 + 6.25

Combine like terms: 109 + 6.25 = 115.25
6.25 + 5x + x2 = 115.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 115.25

Calculate the square root of the right side: 10.735455277

Break this problem into two subproblems by setting 
(x + 2.5) equal to 10.735455277 and -10.735455277.


Subproblem 1
x + 2.5 = 10.735455277

Simplifying
x + 2.5 = 10.735455277

Reorder the terms:
2.5 + x = 10.735455277

Solving
2.5 + x = 10.735455277

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 = 10.735455277 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 10.735455277 + -2.5
x = 10.735455277 + -2.5

Combine like terms: 10.735455277 + -2.5 = 8.235455277
x = 8.235455277

Simplifying
x = 8.235455277


Subproblem 2
x + 2.5 = -10.735455277

Simplifying
x + 2.5 = -10.735455277

Reorder the terms:
2.5 + x = -10.735455277

Solving
2.5 + x = -10.735455277

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 = -10.735455277 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -10.735455277 + -2.5
x = -10.735455277 + -2.5

Combine like terms: -10.735455277 + -2.5 = -13.235455277
x = -13.235455277

Simplifying
x = -13.235455277


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.235455277, -13.235455277}
Solution
x = {8.235455277, -13.235455277}

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