-x^2+16x+15=0

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Solution for -x^2+16x+15=0 equation: 


Simplifying
-1x2 + 16x + 15 = 0

Reorder the terms:
15 + 16x + -1x2 = 0

Solving
15 + 16x + -1x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-15 + -16x + x2 = 0

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + -16x + 15 + x2 = 0 + 15

Reorder the terms:
-15 + 15 + -16x + x2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -16x + x2 = 0 + 15
-16x + x2 = 0 + 15

Combine like terms: 0 + 15 = 15
-16x + x2 = 15

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 = 15 + 64

Reorder the terms:
64 + -16x + x2 = 15 + 64

Combine like terms: 15 + 64 = 79
64 + -16x + x2 = 79

Factor a perfect square on the left side:
(x + -8)(x + -8) = 79

Calculate the square root of the right side: 8.888194417

Break this problem into two subproblems by setting 
(x + -8) equal to 8.888194417 and -8.888194417.


Subproblem 1
x + -8 = 8.888194417

Simplifying
x + -8 = 8.888194417

Reorder the terms:
-8 + x = 8.888194417

Solving
-8 + x = 8.888194417

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 = 8.888194417 + 8

Combine like terms: -8 + 8 = 0
0 + x = 8.888194417 + 8
x = 8.888194417 + 8

Combine like terms: 8.888194417 + 8 = 16.888194417
x = 16.888194417

Simplifying
x = 16.888194417


Subproblem 2
x + -8 = -8.888194417

Simplifying
x + -8 = -8.888194417

Reorder the terms:
-8 + x = -8.888194417

Solving
-8 + x = -8.888194417

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 = -8.888194417 + 8

Combine like terms: -8 + 8 = 0
0 + x = -8.888194417 + 8
x = -8.888194417 + 8

Combine like terms: -8.888194417 + 8 = -0.888194417
x = -0.888194417

Simplifying
x = -0.888194417


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.888194417, -0.888194417}

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