x^2+16x-28=0

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Solution for x^2+16x-28=0 equation: 


Simplifying
x2 + 16x + -28 = 0

Reorder the terms:
-28 + 16x + x2 = 0

Solving
-28 + 16x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '28' to each side of the equation.
-28 + 16x + 28 + x2 = 0 + 28

Reorder the terms:
-28 + 28 + 16x + x2 = 0 + 28

Combine like terms: -28 + 28 = 0
0 + 16x + x2 = 0 + 28
16x + x2 = 0 + 28

Combine like terms: 0 + 28 = 28
16x + x2 = 28

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 = 28 + 64

Reorder the terms:
64 + 16x + x2 = 28 + 64

Combine like terms: 28 + 64 = 92
64 + 16x + x2 = 92

Factor a perfect square on the left side:
(x + 8)(x + 8) = 92

Calculate the square root of the right side: 9.591663047

Break this problem into two subproblems by setting 
(x + 8) equal to 9.591663047 and -9.591663047.


Subproblem 1
x + 8 = 9.591663047

Simplifying
x + 8 = 9.591663047

Reorder the terms:
8 + x = 9.591663047

Solving
8 + x = 9.591663047

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 = 9.591663047 + -8

Combine like terms: 8 + -8 = 0
0 + x = 9.591663047 + -8
x = 9.591663047 + -8

Combine like terms: 9.591663047 + -8 = 1.591663047
x = 1.591663047

Simplifying
x = 1.591663047


Subproblem 2
x + 8 = -9.591663047

Simplifying
x + 8 = -9.591663047

Reorder the terms:
8 + x = -9.591663047

Solving
8 + x = -9.591663047

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 = -9.591663047 + -8

Combine like terms: 8 + -8 = 0
0 + x = -9.591663047 + -8
x = -9.591663047 + -8

Combine like terms: -9.591663047 + -8 = -17.591663047
x = -17.591663047

Simplifying
x = -17.591663047


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.591663047, -17.591663047}

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