-8x^2+163x-65=0

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Solution for -8x^2+163x-65=0 equation: 


Simplifying
-8x2 + 163x + -65 = 0

Reorder the terms:
-65 + 163x + -8x2 = 0

Solving
-65 + 163x + -8x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
8.125 + -20.375x + x2 = 0

Move the constant term to the right:

Add '-8.125' to each side of the equation.
8.125 + -20.375x + -8.125 + x2 = 0 + -8.125

Reorder the terms:
8.125 + -8.125 + -20.375x + x2 = 0 + -8.125

Combine like terms: 8.125 + -8.125 = 0.000
0.000 + -20.375x + x2 = 0 + -8.125
-20.375x + x2 = 0 + -8.125

Combine like terms: 0 + -8.125 = -8.125
-20.375x + x2 = -8.125

The x term is -20.375x.  Take half its coefficient (-10.1875).
Square it (103.7851563) and add it to both sides.

Add '103.7851563' to each side of the equation.
-20.375x + 103.7851563 + x2 = -8.125 + 103.7851563

Reorder the terms:
103.7851563 + -20.375x + x2 = -8.125 + 103.7851563

Combine like terms: -8.125 + 103.7851563 = 95.6601563
103.7851563 + -20.375x + x2 = 95.6601563

Factor a perfect square on the left side:
(x + -10.1875)(x + -10.1875) = 95.6601563

Calculate the square root of the right side: 9.780601019

Break this problem into two subproblems by setting 
(x + -10.1875) equal to 9.780601019 and -9.780601019.


Subproblem 1
x + -10.1875 = 9.780601019

Simplifying
x + -10.1875 = 9.780601019

Reorder the terms:
-10.1875 + x = 9.780601019

Solving
-10.1875 + x = 9.780601019

Solving for variable 'x'.

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

Add '10.1875' to each side of the equation.
-10.1875 + 10.1875 + x = 9.780601019 + 10.1875

Combine like terms: -10.1875 + 10.1875 = 0.0000
0.0000 + x = 9.780601019 + 10.1875
x = 9.780601019 + 10.1875

Combine like terms: 9.780601019 + 10.1875 = 19.968101019
x = 19.968101019

Simplifying
x = 19.968101019


Subproblem 2
x + -10.1875 = -9.780601019

Simplifying
x + -10.1875 = -9.780601019

Reorder the terms:
-10.1875 + x = -9.780601019

Solving
-10.1875 + x = -9.780601019

Solving for variable 'x'.

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

Add '10.1875' to each side of the equation.
-10.1875 + 10.1875 + x = -9.780601019 + 10.1875

Combine like terms: -10.1875 + 10.1875 = 0.0000
0.0000 + x = -9.780601019 + 10.1875
x = -9.780601019 + 10.1875

Combine like terms: -9.780601019 + 10.1875 = 0.406898981
x = 0.406898981

Simplifying
x = 0.406898981


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {19.968101019, 0.406898981}

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