x*x+5x-60=0

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Solution for x*x+5x-60=0 equation: 


Simplifying
x * x + 5x + -60 = 0

Multiply x * x
x2 + 5x + -60 = 0

Reorder the terms:
-60 + 5x + x2 = 0

Solving
-60 + 5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '60' to each side of the equation.
-60 + 5x + 60 + x2 = 0 + 60

Reorder the terms:
-60 + 60 + 5x + x2 = 0 + 60

Combine like terms: -60 + 60 = 0
0 + 5x + x2 = 0 + 60
5x + x2 = 0 + 60

Combine like terms: 0 + 60 = 60
5x + x2 = 60

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 = 60 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 60 + 6.25

Combine like terms: 60 + 6.25 = 66.25
6.25 + 5x + x2 = 66.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 66.25

Calculate the square root of the right side: 8.139410298

Break this problem into two subproblems by setting 
(x + 2.5) equal to 8.139410298 and -8.139410298.


Subproblem 1
x + 2.5 = 8.139410298

Simplifying
x + 2.5 = 8.139410298

Reorder the terms:
2.5 + x = 8.139410298

Solving
2.5 + x = 8.139410298

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 = 8.139410298 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 8.139410298 + -2.5
x = 8.139410298 + -2.5

Combine like terms: 8.139410298 + -2.5 = 5.639410298
x = 5.639410298

Simplifying
x = 5.639410298


Subproblem 2
x + 2.5 = -8.139410298

Simplifying
x + 2.5 = -8.139410298

Reorder the terms:
2.5 + x = -8.139410298

Solving
2.5 + x = -8.139410298

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 = -8.139410298 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -8.139410298 + -2.5
x = -8.139410298 + -2.5

Combine like terms: -8.139410298 + -2.5 = -10.639410298
x = -10.639410298

Simplifying
x = -10.639410298


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.639410298, -10.639410298}

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