x^2+28x+-5=6

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Solution for x^2+28x+-5=6 equation: 


Simplifying
x2 + 28x + -5 = 6

Reorder the terms:
-5 + 28x + x2 = 6

Solving
-5 + 28x + x2 = 6

Solving for variable 'x'.

Reorder the terms:
-5 + -6 + 28x + x2 = 6 + -6

Combine like terms: -5 + -6 = -11
-11 + 28x + x2 = 6 + -6

Combine like terms: 6 + -6 = 0
-11 + 28x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + 28x + 11 + x2 = 0 + 11

Reorder the terms:
-11 + 11 + 28x + x2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + 28x + x2 = 0 + 11
28x + x2 = 0 + 11

Combine like terms: 0 + 11 = 11
28x + x2 = 11

The x term is 28x.  Take half its coefficient (14).
Square it (196) and add it to both sides.

Add '196' to each side of the equation.
28x + 196 + x2 = 11 + 196

Reorder the terms:
196 + 28x + x2 = 11 + 196

Combine like terms: 11 + 196 = 207
196 + 28x + x2 = 207

Factor a perfect square on the left side:
(x + 14)(x + 14) = 207

Calculate the square root of the right side: 14.38749457

Break this problem into two subproblems by setting 
(x + 14) equal to 14.38749457 and -14.38749457.


Subproblem 1
x + 14 = 14.38749457

Simplifying
x + 14 = 14.38749457

Reorder the terms:
14 + x = 14.38749457

Solving
14 + x = 14.38749457

Solving for variable 'x'.

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

Add '-14' to each side of the equation.
14 + -14 + x = 14.38749457 + -14

Combine like terms: 14 + -14 = 0
0 + x = 14.38749457 + -14
x = 14.38749457 + -14

Combine like terms: 14.38749457 + -14 = 0.38749457
x = 0.38749457

Simplifying
x = 0.38749457


Subproblem 2
x + 14 = -14.38749457

Simplifying
x + 14 = -14.38749457

Reorder the terms:
14 + x = -14.38749457

Solving
14 + x = -14.38749457

Solving for variable 'x'.

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

Add '-14' to each side of the equation.
14 + -14 + x = -14.38749457 + -14

Combine like terms: 14 + -14 = 0
0 + x = -14.38749457 + -14
x = -14.38749457 + -14

Combine like terms: -14.38749457 + -14 = -28.38749457
x = -28.38749457

Simplifying
x = -28.38749457


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.38749457, -28.38749457}

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