x^2+5x=79.75

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Solution for x^2+5x=79.75 equation: 


Simplifying
x2 + 5x = 79.75

Reorder the terms:
5x + x2 = 79.75

Solving
5x + x2 = 79.75

Solving for variable 'x'.

Reorder the terms:
-79.75 + 5x + x2 = 79.75 + -79.75

Combine like terms: 79.75 + -79.75 = 0.00
-79.75 + 5x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '79.75' to each side of the equation.
-79.75 + 5x + 79.75 + x2 = 0.00 + 79.75

Reorder the terms:
-79.75 + 79.75 + 5x + x2 = 0.00 + 79.75

Combine like terms: -79.75 + 79.75 = 0.00
0.00 + 5x + x2 = 0.00 + 79.75
5x + x2 = 0.00 + 79.75

Combine like terms: 0.00 + 79.75 = 79.75
5x + x2 = 79.75

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 = 79.75 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 79.75 + 6.25

Combine like terms: 79.75 + 6.25 = 86
6.25 + 5x + x2 = 86

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 86

Calculate the square root of the right side: 9.273618495

Break this problem into two subproblems by setting 
(x + 2.5) equal to 9.273618495 and -9.273618495.


Subproblem 1
x + 2.5 = 9.273618495

Simplifying
x + 2.5 = 9.273618495

Reorder the terms:
2.5 + x = 9.273618495

Solving
2.5 + x = 9.273618495

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 = 9.273618495 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 9.273618495 + -2.5
x = 9.273618495 + -2.5

Combine like terms: 9.273618495 + -2.5 = 6.773618495
x = 6.773618495

Simplifying
x = 6.773618495


Subproblem 2
x + 2.5 = -9.273618495

Simplifying
x + 2.5 = -9.273618495

Reorder the terms:
2.5 + x = -9.273618495

Solving
2.5 + x = -9.273618495

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 = -9.273618495 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -9.273618495 + -2.5
x = -9.273618495 + -2.5

Combine like terms: -9.273618495 + -2.5 = -11.773618495
x = -11.773618495

Simplifying
x = -11.773618495


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.773618495, -11.773618495}

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