x^2-36x-716=0

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Solution for x^2-36x-716=0 equation: 


Simplifying
x2 + -36x + -716 = 0

Reorder the terms:
-716 + -36x + x2 = 0

Solving
-716 + -36x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '716' to each side of the equation.
-716 + -36x + 716 + x2 = 0 + 716

Reorder the terms:
-716 + 716 + -36x + x2 = 0 + 716

Combine like terms: -716 + 716 = 0
0 + -36x + x2 = 0 + 716
-36x + x2 = 0 + 716

Combine like terms: 0 + 716 = 716
-36x + x2 = 716

The x term is -36x.  Take half its coefficient (-18).
Square it (324) and add it to both sides.

Add '324' to each side of the equation.
-36x + 324 + x2 = 716 + 324

Reorder the terms:
324 + -36x + x2 = 716 + 324

Combine like terms: 716 + 324 = 1040
324 + -36x + x2 = 1040

Factor a perfect square on the left side:
(x + -18)(x + -18) = 1040

Calculate the square root of the right side: 32.249030993

Break this problem into two subproblems by setting 
(x + -18) equal to 32.249030993 and -32.249030993.


Subproblem 1
x + -18 = 32.249030993

Simplifying
x + -18 = 32.249030993

Reorder the terms:
-18 + x = 32.249030993

Solving
-18 + x = 32.249030993

Solving for variable 'x'.

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

Add '18' to each side of the equation.
-18 + 18 + x = 32.249030993 + 18

Combine like terms: -18 + 18 = 0
0 + x = 32.249030993 + 18
x = 32.249030993 + 18

Combine like terms: 32.249030993 + 18 = 50.249030993
x = 50.249030993

Simplifying
x = 50.249030993


Subproblem 2
x + -18 = -32.249030993

Simplifying
x + -18 = -32.249030993

Reorder the terms:
-18 + x = -32.249030993

Solving
-18 + x = -32.249030993

Solving for variable 'x'.

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

Add '18' to each side of the equation.
-18 + 18 + x = -32.249030993 + 18

Combine like terms: -18 + 18 = 0
0 + x = -32.249030993 + 18
x = -32.249030993 + 18

Combine like terms: -32.249030993 + 18 = -14.249030993
x = -14.249030993

Simplifying
x = -14.249030993


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {50.249030993, -14.249030993}

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