6x^2-100x+144=0

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Solution for 6x^2-100x+144=0 equation: 


Simplifying
6x2 + -100x + 144 = 0

Reorder the terms:
144 + -100x + 6x2 = 0

Solving
144 + -100x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(72 + -50x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(72 + -50x + 3x2)' equal to zero and attempt to solve:

Simplifying
72 + -50x + 3x2 = 0

Solving
72 + -50x + 3x2 = 0

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

Divide each side by '3'.
24 + -16.66666667x + x2 = 0

Move the constant term to the right:

Add '-24' to each side of the equation.
24 + -16.66666667x + -24 + x2 = 0 + -24

Reorder the terms:
24 + -24 + -16.66666667x + x2 = 0 + -24

Combine like terms: 24 + -24 = 0
0 + -16.66666667x + x2 = 0 + -24
-16.66666667x + x2 = 0 + -24

Combine like terms: 0 + -24 = -24
-16.66666667x + x2 = -24

The x term is -16.66666667x.  Take half its coefficient (-8.333333335).
Square it (69.44444447) and add it to both sides.

Add '69.44444447' to each side of the equation.
-16.66666667x + 69.44444447 + x2 = -24 + 69.44444447

Reorder the terms:
69.44444447 + -16.66666667x + x2 = -24 + 69.44444447

Combine like terms: -24 + 69.44444447 = 45.44444447
69.44444447 + -16.66666667x + x2 = 45.44444447

Factor a perfect square on the left side:
(x + -8.333333335)(x + -8.333333335) = 45.44444447

Calculate the square root of the right side: 6.741249474

Break this problem into two subproblems by setting 
(x + -8.333333335) equal to 6.741249474 and -6.741249474.


Subproblem 1
x + -8.333333335 = 6.741249474

Simplifying
x + -8.333333335 = 6.741249474

Reorder the terms:
-8.333333335 + x = 6.741249474

Solving
-8.333333335 + x = 6.741249474

Solving for variable 'x'.

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

Add '8.333333335' to each side of the equation.
-8.333333335 + 8.333333335 + x = 6.741249474 + 8.333333335

Combine like terms: -8.333333335 + 8.333333335 = 0.000000000
0.000000000 + x = 6.741249474 + 8.333333335
x = 6.741249474 + 8.333333335

Combine like terms: 6.741249474 + 8.333333335 = 15.074582809
x = 15.074582809

Simplifying
x = 15.074582809


Subproblem 2
x + -8.333333335 = -6.741249474

Simplifying
x + -8.333333335 = -6.741249474

Reorder the terms:
-8.333333335 + x = -6.741249474

Solving
-8.333333335 + x = -6.741249474

Solving for variable 'x'.

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

Add '8.333333335' to each side of the equation.
-8.333333335 + 8.333333335 + x = -6.741249474 + 8.333333335

Combine like terms: -8.333333335 + 8.333333335 = 0.000000000
0.000000000 + x = -6.741249474 + 8.333333335
x = -6.741249474 + 8.333333335

Combine like terms: -6.741249474 + 8.333333335 = 1.592083861
x = 1.592083861

Simplifying
x = 1.592083861


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15.074582809, 1.592083861}
Solution
x = {15.074582809, 1.592083861}

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