6x^2-96x+37=0

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Solution for 6x^2-96x+37=0 equation: 


Simplifying
6x2 + -96x + 37 = 0

Reorder the terms:
37 + -96x + 6x2 = 0

Solving
37 + -96x + 6x2 = 0

Solving for variable 'x'.

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

Divide each side by '6'.
6.166666667 + -16x + x2 = 0

Move the constant term to the right:

Add '-6.166666667' to each side of the equation.
6.166666667 + -16x + -6.166666667 + x2 = 0 + -6.166666667

Reorder the terms:
6.166666667 + -6.166666667 + -16x + x2 = 0 + -6.166666667

Combine like terms: 6.166666667 + -6.166666667 = 0.000000000
0.000000000 + -16x + x2 = 0 + -6.166666667
-16x + x2 = 0 + -6.166666667

Combine like terms: 0 + -6.166666667 = -6.166666667
-16x + x2 = -6.166666667

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 = -6.166666667 + 64

Reorder the terms:
64 + -16x + x2 = -6.166666667 + 64

Combine like terms: -6.166666667 + 64 = 57.833333333
64 + -16x + x2 = 57.833333333

Factor a perfect square on the left side:
(x + -8)(x + -8) = 57.833333333

Calculate the square root of the right side: 7.604823031

Break this problem into two subproblems by setting 
(x + -8) equal to 7.604823031 and -7.604823031.


Subproblem 1
x + -8 = 7.604823031

Simplifying
x + -8 = 7.604823031

Reorder the terms:
-8 + x = 7.604823031

Solving
-8 + x = 7.604823031

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 = 7.604823031 + 8

Combine like terms: -8 + 8 = 0
0 + x = 7.604823031 + 8
x = 7.604823031 + 8

Combine like terms: 7.604823031 + 8 = 15.604823031
x = 15.604823031

Simplifying
x = 15.604823031


Subproblem 2
x + -8 = -7.604823031

Simplifying
x + -8 = -7.604823031

Reorder the terms:
-8 + x = -7.604823031

Solving
-8 + x = -7.604823031

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 = -7.604823031 + 8

Combine like terms: -8 + 8 = 0
0 + x = -7.604823031 + 8
x = -7.604823031 + 8

Combine like terms: -7.604823031 + 8 = 0.395176969
x = 0.395176969

Simplifying
x = 0.395176969


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15.604823031, 0.395176969}

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