x^2-16x-2=-9

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Solution for x^2-16x-2=-9 equation: 


Simplifying
x2 + -16x + -2 = -9

Reorder the terms:
-2 + -16x + x2 = -9

Solving
-2 + -16x + x2 = -9

Solving for variable 'x'.

Reorder the terms:
-2 + 9 + -16x + x2 = -9 + 9

Combine like terms: -2 + 9 = 7
7 + -16x + x2 = -9 + 9

Combine like terms: -9 + 9 = 0
7 + -16x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + -16x + -7 + x2 = 0 + -7

Reorder the terms:
7 + -7 + -16x + x2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -16x + x2 = 0 + -7
-16x + x2 = 0 + -7

Combine like terms: 0 + -7 = -7
-16x + x2 = -7

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 = -7 + 64

Reorder the terms:
64 + -16x + x2 = -7 + 64

Combine like terms: -7 + 64 = 57
64 + -16x + x2 = 57

Factor a perfect square on the left side:
(x + -8)(x + -8) = 57

Calculate the square root of the right side: 7.549834435

Break this problem into two subproblems by setting 
(x + -8) equal to 7.549834435 and -7.549834435.


Subproblem 1
x + -8 = 7.549834435

Simplifying
x + -8 = 7.549834435

Reorder the terms:
-8 + x = 7.549834435

Solving
-8 + x = 7.549834435

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 = 7.549834435 + 8

Combine like terms: -8 + 8 = 0
0 + x = 7.549834435 + 8
x = 7.549834435 + 8

Combine like terms: 7.549834435 + 8 = 15.549834435
x = 15.549834435

Simplifying
x = 15.549834435


Subproblem 2
x + -8 = -7.549834435

Simplifying
x + -8 = -7.549834435

Reorder the terms:
-8 + x = -7.549834435

Solving
-8 + x = -7.549834435

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 = -7.549834435 + 8

Combine like terms: -8 + 8 = 0
0 + x = -7.549834435 + 8
x = -7.549834435 + 8

Combine like terms: -7.549834435 + 8 = 0.450165565
x = 0.450165565

Simplifying
x = 0.450165565


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15.549834435, 0.450165565}

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