x^2+25x-36=0

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Solution for x^2+25x-36=0 equation:


Simplifying
x2 + 25x + -36 = 0

Reorder the terms:
-36 + 25x + x2 = 0

Solving
-36 + 25x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + 25x + 36 + x2 = 0 + 36

Reorder the terms:
-36 + 36 + 25x + x2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + 25x + x2 = 0 + 36
25x + x2 = 0 + 36

Combine like terms: 0 + 36 = 36
25x + x2 = 36

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 = 36 + 156.25

Reorder the terms:
156.25 + 25x + x2 = 36 + 156.25

Combine like terms: 36 + 156.25 = 192.25
156.25 + 25x + x2 = 192.25

Factor a perfect square on the left side:
(x + 12.5)(x + 12.5) = 192.25

Calculate the square root of the right side: 13.865424624

Break this problem into two subproblems by setting 
(x + 12.5) equal to 13.865424624 and -13.865424624.


Subproblem 1
x + 12.5 = 13.865424624

Simplifying
x + 12.5 = 13.865424624

Reorder the terms:
12.5 + x = 13.865424624

Solving
12.5 + x = 13.865424624

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 = 13.865424624 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + x = 13.865424624 + -12.5
x = 13.865424624 + -12.5

Combine like terms: 13.865424624 + -12.5 = 1.365424624
x = 1.365424624

Simplifying
x = 1.365424624


Subproblem 2
x + 12.5 = -13.865424624

Simplifying
x + 12.5 = -13.865424624

Reorder the terms:
12.5 + x = -13.865424624

Solving
12.5 + x = -13.865424624

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 = -13.865424624 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + x = -13.865424624 + -12.5
x = -13.865424624 + -12.5

Combine like terms: -13.865424624 + -12.5 = -26.365424624
x = -26.365424624

Simplifying
x = -26.365424624


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.365424624, -26.365424624}

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