x^2+16x-11=0

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Solution for x^2+16x-11=0 equation:


Simplifying
x2 + 16x + -11 = 0

Reorder the terms:
-11 + 16x + x2 = 0

Solving
-11 + 16x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + 16x + 11 + x2 = 0 + 11

Reorder the terms:
-11 + 11 + 16x + x2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + 16x + x2 = 0 + 11
16x + x2 = 0 + 11

Combine like terms: 0 + 11 = 11
16x + x2 = 11

The x term is 16x.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16x + 64 + x2 = 11 + 64

Reorder the terms:
64 + 16x + x2 = 11 + 64

Combine like terms: 11 + 64 = 75
64 + 16x + x2 = 75

Factor a perfect square on the left side:
(x + 8)(x + 8) = 75

Calculate the square root of the right side: 8.660254038

Break this problem into two subproblems by setting 
(x + 8) equal to 8.660254038 and -8.660254038.


Subproblem 1
x + 8 = 8.660254038

Simplifying
x + 8 = 8.660254038

Reorder the terms:
8 + x = 8.660254038

Solving
8 + x = 8.660254038

Solving for variable 'x'.

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

Add '-8' to each side of the equation.
8 + -8 + x = 8.660254038 + -8

Combine like terms: 8 + -8 = 0
0 + x = 8.660254038 + -8
x = 8.660254038 + -8

Combine like terms: 8.660254038 + -8 = 0.660254038
x = 0.660254038

Simplifying
x = 0.660254038


Subproblem 2
x + 8 = -8.660254038

Simplifying
x + 8 = -8.660254038

Reorder the terms:
8 + x = -8.660254038

Solving
8 + x = -8.660254038

Solving for variable 'x'.

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

Add '-8' to each side of the equation.
8 + -8 + x = -8.660254038 + -8

Combine like terms: 8 + -8 = 0
0 + x = -8.660254038 + -8
x = -8.660254038 + -8

Combine like terms: -8.660254038 + -8 = -16.660254038
x = -16.660254038

Simplifying
x = -16.660254038


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.660254038, -16.660254038}

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