x^2+7x-216=0

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Solution for x^2+7x-216=0 equation: 


Simplifying
x2 + 7x + -216 = 0

Reorder the terms:
-216 + 7x + x2 = 0

Solving
-216 + 7x + 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 + 7x + 216 + x2 = 0 + 216

Reorder the terms:
-216 + 216 + 7x + x2 = 0 + 216

Combine like terms: -216 + 216 = 0
0 + 7x + x2 = 0 + 216
7x + x2 = 0 + 216

Combine like terms: 0 + 216 = 216
7x + x2 = 216

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = 216 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 216 + 12.25

Combine like terms: 216 + 12.25 = 228.25
12.25 + 7x + x2 = 228.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 228.25

Calculate the square root of the right side: 15.10794493

Break this problem into two subproblems by setting 
(x + 3.5) equal to 15.10794493 and -15.10794493.


Subproblem 1
x + 3.5 = 15.10794493

Simplifying
x + 3.5 = 15.10794493

Reorder the terms:
3.5 + x = 15.10794493

Solving
3.5 + x = 15.10794493

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = 15.10794493 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 15.10794493 + -3.5
x = 15.10794493 + -3.5

Combine like terms: 15.10794493 + -3.5 = 11.60794493
x = 11.60794493

Simplifying
x = 11.60794493


Subproblem 2
x + 3.5 = -15.10794493

Simplifying
x + 3.5 = -15.10794493

Reorder the terms:
3.5 + x = -15.10794493

Solving
3.5 + x = -15.10794493

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = -15.10794493 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -15.10794493 + -3.5
x = -15.10794493 + -3.5

Combine like terms: -15.10794493 + -3.5 = -18.60794493
x = -18.60794493

Simplifying
x = -18.60794493


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.60794493, -18.60794493}

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