x^2+35x-216=0

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Solution for x^2+35x-216=0 equation: 


Simplifying
x2 + 35x + -216 = 0

Reorder the terms:
-216 + 35x + x2 = 0

Solving
-216 + 35x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '216' to each side of the equation.
-216 + 35x + 216 + x2 = 0 + 216

Reorder the terms:
-216 + 216 + 35x + x2 = 0 + 216

Combine like terms: -216 + 216 = 0
0 + 35x + x2 = 0 + 216
35x + x2 = 0 + 216

Combine like terms: 0 + 216 = 216
35x + x2 = 216

The x term is 35x.  Take half its coefficient (17.5).
Square it (306.25) and add it to both sides.

Add '306.25' to each side of the equation.
35x + 306.25 + x2 = 216 + 306.25

Reorder the terms:
306.25 + 35x + x2 = 216 + 306.25

Combine like terms: 216 + 306.25 = 522.25
306.25 + 35x + x2 = 522.25

Factor a perfect square on the left side:
(x + 17.5)(x + 17.5) = 522.25

Calculate the square root of the right side: 22.852789764

Break this problem into two subproblems by setting 
(x + 17.5) equal to 22.852789764 and -22.852789764.


Subproblem 1
x + 17.5 = 22.852789764

Simplifying
x + 17.5 = 22.852789764

Reorder the terms:
17.5 + x = 22.852789764

Solving
17.5 + x = 22.852789764

Solving for variable 'x'.

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

Add '-17.5' to each side of the equation.
17.5 + -17.5 + x = 22.852789764 + -17.5

Combine like terms: 17.5 + -17.5 = 0.0
0.0 + x = 22.852789764 + -17.5
x = 22.852789764 + -17.5

Combine like terms: 22.852789764 + -17.5 = 5.352789764
x = 5.352789764

Simplifying
x = 5.352789764


Subproblem 2
x + 17.5 = -22.852789764

Simplifying
x + 17.5 = -22.852789764

Reorder the terms:
17.5 + x = -22.852789764

Solving
17.5 + x = -22.852789764

Solving for variable 'x'.

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

Add '-17.5' to each side of the equation.
17.5 + -17.5 + x = -22.852789764 + -17.5

Combine like terms: 17.5 + -17.5 = 0.0
0.0 + x = -22.852789764 + -17.5
x = -22.852789764 + -17.5

Combine like terms: -22.852789764 + -17.5 = -40.352789764
x = -40.352789764

Simplifying
x = -40.352789764


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.352789764, -40.352789764}

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