(x*x)+25x-60=0

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Solution for (x*x)+25x-60=0 equation: 


Simplifying
(x * x) + 25x + -60 = 0

Multiply x * x
(x2) + 25x + -60 = 0
x2 + 25x + -60 = 0

Reorder the terms:
-60 + 25x + x2 = 0

Solving
-60 + 25x + 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 + 25x + 60 + x2 = 0 + 60

Reorder the terms:
-60 + 60 + 25x + x2 = 0 + 60

Combine like terms: -60 + 60 = 0
0 + 25x + x2 = 0 + 60
25x + x2 = 0 + 60

Combine like terms: 0 + 60 = 60
25x + x2 = 60

The x term is 25x.  Take half its coefficient (12.5).
Square it (156.25) and add it to both sides.

Add '156.25' to each side of the equation.
25x + 156.25 + x2 = 60 + 156.25

Reorder the terms:
156.25 + 25x + x2 = 60 + 156.25

Combine like terms: 60 + 156.25 = 216.25
156.25 + 25x + x2 = 216.25

Factor a perfect square on the left side:
(x + 12.5)(x + 12.5) = 216.25

Calculate the square root of the right side: 14.70544117

Break this problem into two subproblems by setting 
(x + 12.5) equal to 14.70544117 and -14.70544117.


Subproblem 1
x + 12.5 = 14.70544117

Simplifying
x + 12.5 = 14.70544117

Reorder the terms:
12.5 + x = 14.70544117

Solving
12.5 + x = 14.70544117

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-12.5' to each side of the equation.
12.5 + -12.5 + x = 14.70544117 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + x = 14.70544117 + -12.5
x = 14.70544117 + -12.5

Combine like terms: 14.70544117 + -12.5 = 2.20544117
x = 2.20544117

Simplifying
x = 2.20544117


Subproblem 2
x + 12.5 = -14.70544117

Simplifying
x + 12.5 = -14.70544117

Reorder the terms:
12.5 + x = -14.70544117

Solving
12.5 + x = -14.70544117

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-12.5' to each side of the equation.
12.5 + -12.5 + x = -14.70544117 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + x = -14.70544117 + -12.5
x = -14.70544117 + -12.5

Combine like terms: -14.70544117 + -12.5 = -27.20544117
x = -27.20544117

Simplifying
x = -27.20544117


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.20544117, -27.20544117}

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