x^2+5x-6750=0

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Solution for x^2+5x-6750=0 equation: 


Simplifying
x2 + 5x + -6750 = 0

Reorder the terms:
-6750 + 5x + x2 = 0

Solving
-6750 + 5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '6750' to each side of the equation.
-6750 + 5x + 6750 + x2 = 0 + 6750

Reorder the terms:
-6750 + 6750 + 5x + x2 = 0 + 6750

Combine like terms: -6750 + 6750 = 0
0 + 5x + x2 = 0 + 6750
5x + x2 = 0 + 6750

Combine like terms: 0 + 6750 = 6750
5x + x2 = 6750

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 = 6750 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 6750 + 6.25

Combine like terms: 6750 + 6.25 = 6756.25
6.25 + 5x + x2 = 6756.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 6756.25

Calculate the square root of the right side: 82.196411114

Break this problem into two subproblems by setting 
(x + 2.5) equal to 82.196411114 and -82.196411114.


Subproblem 1
x + 2.5 = 82.196411114

Simplifying
x + 2.5 = 82.196411114

Reorder the terms:
2.5 + x = 82.196411114

Solving
2.5 + x = 82.196411114

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 = 82.196411114 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 82.196411114 + -2.5
x = 82.196411114 + -2.5

Combine like terms: 82.196411114 + -2.5 = 79.696411114
x = 79.696411114

Simplifying
x = 79.696411114


Subproblem 2
x + 2.5 = -82.196411114

Simplifying
x + 2.5 = -82.196411114

Reorder the terms:
2.5 + x = -82.196411114

Solving
2.5 + x = -82.196411114

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 = -82.196411114 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -82.196411114 + -2.5
x = -82.196411114 + -2.5

Combine like terms: -82.196411114 + -2.5 = -84.696411114
x = -84.696411114

Simplifying
x = -84.696411114


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {79.696411114, -84.696411114}

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