16x^2-88x-161=0

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Solution for 16x^2-88x-161=0 equation: 


Simplifying
16x2 + -88x + -161 = 0

Reorder the terms:
-161 + -88x + 16x2 = 0

Solving
-161 + -88x + 16x2 = 0

Solving for variable 'x'.

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

Divide each side by '16'.
-10.0625 + -5.5x + x2 = 0

Move the constant term to the right:

Add '10.0625' to each side of the equation.
-10.0625 + -5.5x + 10.0625 + x2 = 0 + 10.0625

Reorder the terms:
-10.0625 + 10.0625 + -5.5x + x2 = 0 + 10.0625

Combine like terms: -10.0625 + 10.0625 = 0.0000
0.0000 + -5.5x + x2 = 0 + 10.0625
-5.5x + x2 = 0 + 10.0625

Combine like terms: 0 + 10.0625 = 10.0625
-5.5x + x2 = 10.0625

The x term is -5.5x.  Take half its coefficient (-2.75).
Square it (7.5625) and add it to both sides.

Add '7.5625' to each side of the equation.
-5.5x + 7.5625 + x2 = 10.0625 + 7.5625

Reorder the terms:
7.5625 + -5.5x + x2 = 10.0625 + 7.5625

Combine like terms: 10.0625 + 7.5625 = 17.625
7.5625 + -5.5x + x2 = 17.625

Factor a perfect square on the left side:
(x + -2.75)(x + -2.75) = 17.625

Calculate the square root of the right side: 4.198213906

Break this problem into two subproblems by setting 
(x + -2.75) equal to 4.198213906 and -4.198213906.


Subproblem 1
x + -2.75 = 4.198213906

Simplifying
x + -2.75 = 4.198213906

Reorder the terms:
-2.75 + x = 4.198213906

Solving
-2.75 + x = 4.198213906

Solving for variable 'x'.

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

Add '2.75' to each side of the equation.
-2.75 + 2.75 + x = 4.198213906 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + x = 4.198213906 + 2.75
x = 4.198213906 + 2.75

Combine like terms: 4.198213906 + 2.75 = 6.948213906
x = 6.948213906

Simplifying
x = 6.948213906


Subproblem 2
x + -2.75 = -4.198213906

Simplifying
x + -2.75 = -4.198213906

Reorder the terms:
-2.75 + x = -4.198213906

Solving
-2.75 + x = -4.198213906

Solving for variable 'x'.

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

Add '2.75' to each side of the equation.
-2.75 + 2.75 + x = -4.198213906 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + x = -4.198213906 + 2.75
x = -4.198213906 + 2.75

Combine like terms: -4.198213906 + 2.75 = -1.448213906
x = -1.448213906

Simplifying
x = -1.448213906


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.948213906, -1.448213906}

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