x^2+5x-57.75=0

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Solution for x^2+5x-57.75=0 equation: 


Simplifying
x2 + 5x + -57.75 = 0

Reorder the terms:
-57.75 + 5x + x2 = 0

Solving
-57.75 + 5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '57.75' to each side of the equation.
-57.75 + 5x + 57.75 + x2 = 0 + 57.75

Reorder the terms:
-57.75 + 57.75 + 5x + x2 = 0 + 57.75

Combine like terms: -57.75 + 57.75 = 0.00
0.00 + 5x + x2 = 0 + 57.75
5x + x2 = 0 + 57.75

Combine like terms: 0 + 57.75 = 57.75
5x + x2 = 57.75

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 = 57.75 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 57.75 + 6.25

Combine like terms: 57.75 + 6.25 = 64
6.25 + 5x + x2 = 64

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 64

Calculate the square root of the right side: 8

Break this problem into two subproblems by setting 
(x + 2.5) equal to 8 and -8.


Subproblem 1
x + 2.5 = 8

Simplifying
x + 2.5 = 8

Reorder the terms:
2.5 + x = 8

Solving
2.5 + x = 8

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 = 8 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 8 + -2.5
x = 8 + -2.5

Combine like terms: 8 + -2.5 = 5.5
x = 5.5

Simplifying
x = 5.5


Subproblem 2
x + 2.5 = -8

Simplifying
x + 2.5 = -8

Reorder the terms:
2.5 + x = -8

Solving
2.5 + x = -8

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 = -8 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -8 + -2.5
x = -8 + -2.5

Combine like terms: -8 + -2.5 = -10.5
x = -10.5

Simplifying
x = -10.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.5, -10.5}

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