x^2+50x-60=0

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Solution for x^2+50x-60=0 equation: 


Simplifying
x2 + 50x + -60 = 0

Reorder the terms:
-60 + 50x + x2 = 0

Solving
-60 + 50x + 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 + 50x + 60 + x2 = 0 + 60

Reorder the terms:
-60 + 60 + 50x + x2 = 0 + 60

Combine like terms: -60 + 60 = 0
0 + 50x + x2 = 0 + 60
50x + x2 = 0 + 60

Combine like terms: 0 + 60 = 60
50x + x2 = 60

The x term is 50x.  Take half its coefficient (25).
Square it (625) and add it to both sides.

Add '625' to each side of the equation.
50x + 625 + x2 = 60 + 625

Reorder the terms:
625 + 50x + x2 = 60 + 625

Combine like terms: 60 + 625 = 685
625 + 50x + x2 = 685

Factor a perfect square on the left side:
(x + 25)(x + 25) = 685

Calculate the square root of the right side: 26.172504657

Break this problem into two subproblems by setting 
(x + 25) equal to 26.172504657 and -26.172504657.


Subproblem 1
x + 25 = 26.172504657

Simplifying
x + 25 = 26.172504657

Reorder the terms:
25 + x = 26.172504657

Solving
25 + x = 26.172504657

Solving for variable 'x'.

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

Add '-25' to each side of the equation.
25 + -25 + x = 26.172504657 + -25

Combine like terms: 25 + -25 = 0
0 + x = 26.172504657 + -25
x = 26.172504657 + -25

Combine like terms: 26.172504657 + -25 = 1.172504657
x = 1.172504657

Simplifying
x = 1.172504657


Subproblem 2
x + 25 = -26.172504657

Simplifying
x + 25 = -26.172504657

Reorder the terms:
25 + x = -26.172504657

Solving
25 + x = -26.172504657

Solving for variable 'x'.

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

Add '-25' to each side of the equation.
25 + -25 + x = -26.172504657 + -25

Combine like terms: 25 + -25 = 0
0 + x = -26.172504657 + -25
x = -26.172504657 + -25

Combine like terms: -26.172504657 + -25 = -51.172504657
x = -51.172504657

Simplifying
x = -51.172504657


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.172504657, -51.172504657}

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