x^2-18x-16=0

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Solution for x^2-18x-16=0 equation: 


Simplifying
x2 + -18x + -16 = 0

Reorder the terms:
-16 + -18x + x2 = 0

Solving
-16 + -18x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + -18x + 16 + x2 = 0 + 16

Reorder the terms:
-16 + 16 + -18x + x2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -18x + x2 = 0 + 16
-18x + x2 = 0 + 16

Combine like terms: 0 + 16 = 16
-18x + x2 = 16

The x term is -18x.  Take half its coefficient (-9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
-18x + 81 + x2 = 16 + 81

Reorder the terms:
81 + -18x + x2 = 16 + 81

Combine like terms: 16 + 81 = 97
81 + -18x + x2 = 97

Factor a perfect square on the left side:
(x + -9)(x + -9) = 97

Calculate the square root of the right side: 9.848857802

Break this problem into two subproblems by setting 
(x + -9) equal to 9.848857802 and -9.848857802.


Subproblem 1
x + -9 = 9.848857802

Simplifying
x + -9 = 9.848857802

Reorder the terms:
-9 + x = 9.848857802

Solving
-9 + x = 9.848857802

Solving for variable 'x'.

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

Add '9' to each side of the equation.
-9 + 9 + x = 9.848857802 + 9

Combine like terms: -9 + 9 = 0
0 + x = 9.848857802 + 9
x = 9.848857802 + 9

Combine like terms: 9.848857802 + 9 = 18.848857802
x = 18.848857802

Simplifying
x = 18.848857802


Subproblem 2
x + -9 = -9.848857802

Simplifying
x + -9 = -9.848857802

Reorder the terms:
-9 + x = -9.848857802

Solving
-9 + x = -9.848857802

Solving for variable 'x'.

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

Add '9' to each side of the equation.
-9 + 9 + x = -9.848857802 + 9

Combine like terms: -9 + 9 = 0
0 + x = -9.848857802 + 9
x = -9.848857802 + 9

Combine like terms: -9.848857802 + 9 = -0.848857802
x = -0.848857802

Simplifying
x = -0.848857802


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {18.848857802, -0.848857802}

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