2x^2-14x-218=0

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Solution for 2x^2-14x-218=0 equation: 


Simplifying
2x2 + -14x + -218 = 0

Reorder the terms:
-218 + -14x + 2x2 = 0

Solving
-218 + -14x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-109 + -7x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-109 + -7x + x2)' equal to zero and attempt to solve:

Simplifying
-109 + -7x + x2 = 0

Solving
-109 + -7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '109' to each side of the equation.
-109 + -7x + 109 + x2 = 0 + 109

Reorder the terms:
-109 + 109 + -7x + x2 = 0 + 109

Combine like terms: -109 + 109 = 0
0 + -7x + x2 = 0 + 109
-7x + x2 = 0 + 109

Combine like terms: 0 + 109 = 109
-7x + x2 = 109

The x term is -7x.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7x + 12.25 + x2 = 109 + 12.25

Reorder the terms:
12.25 + -7x + x2 = 109 + 12.25

Combine like terms: 109 + 12.25 = 121.25
12.25 + -7x + x2 = 121.25

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 121.25

Calculate the square root of the right side: 11.011357773

Break this problem into two subproblems by setting 
(x + -3.5) equal to 11.011357773 and -11.011357773.


Subproblem 1
x + -3.5 = 11.011357773

Simplifying
x + -3.5 = 11.011357773

Reorder the terms:
-3.5 + x = 11.011357773

Solving
-3.5 + x = 11.011357773

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = 11.011357773 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = 11.011357773 + 3.5
x = 11.011357773 + 3.5

Combine like terms: 11.011357773 + 3.5 = 14.511357773
x = 14.511357773

Simplifying
x = 14.511357773


Subproblem 2
x + -3.5 = -11.011357773

Simplifying
x + -3.5 = -11.011357773

Reorder the terms:
-3.5 + x = -11.011357773

Solving
-3.5 + x = -11.011357773

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = -11.011357773 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = -11.011357773 + 3.5
x = -11.011357773 + 3.5

Combine like terms: -11.011357773 + 3.5 = -7.511357773
x = -7.511357773

Simplifying
x = -7.511357773


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.511357773, -7.511357773}
Solution
x = {14.511357773, -7.511357773}

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