x^2+5x=85.25

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Solution for x^2+5x=85.25 equation: 


Simplifying
x2 + 5x = 85.25

Reorder the terms:
5x + x2 = 85.25

Solving
5x + x2 = 85.25

Solving for variable 'x'.

Reorder the terms:
-85.25 + 5x + x2 = 85.25 + -85.25

Combine like terms: 85.25 + -85.25 = 0.00
-85.25 + 5x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '85.25' to each side of the equation.
-85.25 + 5x + 85.25 + x2 = 0.00 + 85.25

Reorder the terms:
-85.25 + 85.25 + 5x + x2 = 0.00 + 85.25

Combine like terms: -85.25 + 85.25 = 0.00
0.00 + 5x + x2 = 0.00 + 85.25
5x + x2 = 0.00 + 85.25

Combine like terms: 0.00 + 85.25 = 85.25
5x + x2 = 85.25

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 = 85.25 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 85.25 + 6.25

Combine like terms: 85.25 + 6.25 = 91.5
6.25 + 5x + x2 = 91.5

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 91.5

Calculate the square root of the right side: 9.565563235

Break this problem into two subproblems by setting 
(x + 2.5) equal to 9.565563235 and -9.565563235.


Subproblem 1
x + 2.5 = 9.565563235

Simplifying
x + 2.5 = 9.565563235

Reorder the terms:
2.5 + x = 9.565563235

Solving
2.5 + x = 9.565563235

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 = 9.565563235 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 9.565563235 + -2.5
x = 9.565563235 + -2.5

Combine like terms: 9.565563235 + -2.5 = 7.065563235
x = 7.065563235

Simplifying
x = 7.065563235


Subproblem 2
x + 2.5 = -9.565563235

Simplifying
x + 2.5 = -9.565563235

Reorder the terms:
2.5 + x = -9.565563235

Solving
2.5 + x = -9.565563235

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 = -9.565563235 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -9.565563235 + -2.5
x = -9.565563235 + -2.5

Combine like terms: -9.565563235 + -2.5 = -12.065563235
x = -12.065563235

Simplifying
x = -12.065563235


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.065563235, -12.065563235}

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