x^2+5x-110=0

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Solution for x^2+5x-110=0 equation: 


Simplifying
x2 + 5x + -110 = 0

Reorder the terms:
-110 + 5x + x2 = 0

Solving
-110 + 5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '110' to each side of the equation.
-110 + 5x + 110 + x2 = 0 + 110

Reorder the terms:
-110 + 110 + 5x + x2 = 0 + 110

Combine like terms: -110 + 110 = 0
0 + 5x + x2 = 0 + 110
5x + x2 = 0 + 110

Combine like terms: 0 + 110 = 110
5x + x2 = 110

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 = 110 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 110 + 6.25

Combine like terms: 110 + 6.25 = 116.25
6.25 + 5x + x2 = 116.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 116.25

Calculate the square root of the right side: 10.781929326

Break this problem into two subproblems by setting 
(x + 2.5) equal to 10.781929326 and -10.781929326.


Subproblem 1
x + 2.5 = 10.781929326

Simplifying
x + 2.5 = 10.781929326

Reorder the terms:
2.5 + x = 10.781929326

Solving
2.5 + x = 10.781929326

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 = 10.781929326 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 10.781929326 + -2.5
x = 10.781929326 + -2.5

Combine like terms: 10.781929326 + -2.5 = 8.281929326
x = 8.281929326

Simplifying
x = 8.281929326


Subproblem 2
x + 2.5 = -10.781929326

Simplifying
x + 2.5 = -10.781929326

Reorder the terms:
2.5 + x = -10.781929326

Solving
2.5 + x = -10.781929326

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 = -10.781929326 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -10.781929326 + -2.5
x = -10.781929326 + -2.5

Combine like terms: -10.781929326 + -2.5 = -13.281929326
x = -13.281929326

Simplifying
x = -13.281929326


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.281929326, -13.281929326}

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