12x^2-80x+99=0

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Solution for 12x^2-80x+99=0 equation: 


Simplifying
12x2 + -80x + 99 = 0

Reorder the terms:
99 + -80x + 12x2 = 0

Solving
99 + -80x + 12x2 = 0

Solving for variable 'x'.

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

Divide each side by '12'.
8.25 + -6.666666667x + x2 = 0

Move the constant term to the right:

Add '-8.25' to each side of the equation.
8.25 + -6.666666667x + -8.25 + x2 = 0 + -8.25

Reorder the terms:
8.25 + -8.25 + -6.666666667x + x2 = 0 + -8.25

Combine like terms: 8.25 + -8.25 = 0.00
0.00 + -6.666666667x + x2 = 0 + -8.25
-6.666666667x + x2 = 0 + -8.25

Combine like terms: 0 + -8.25 = -8.25
-6.666666667x + x2 = -8.25

The x term is -6.666666667x.  Take half its coefficient (-3.333333334).
Square it (11.11111112) and add it to both sides.

Add '11.11111112' to each side of the equation.
-6.666666667x + 11.11111112 + x2 = -8.25 + 11.11111112

Reorder the terms:
11.11111112 + -6.666666667x + x2 = -8.25 + 11.11111112

Combine like terms: -8.25 + 11.11111112 = 2.86111112
11.11111112 + -6.666666667x + x2 = 2.86111112

Factor a perfect square on the left side:
(x + -3.333333334)(x + -3.333333334) = 2.86111112

Calculate the square root of the right side: 1.69148193

Break this problem into two subproblems by setting 
(x + -3.333333334) equal to 1.69148193 and -1.69148193.


Subproblem 1
x + -3.333333334 = 1.69148193

Simplifying
x + -3.333333334 = 1.69148193

Reorder the terms:
-3.333333334 + x = 1.69148193

Solving
-3.333333334 + x = 1.69148193

Solving for variable 'x'.

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

Add '3.333333334' to each side of the equation.
-3.333333334 + 3.333333334 + x = 1.69148193 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + x = 1.69148193 + 3.333333334
x = 1.69148193 + 3.333333334

Combine like terms: 1.69148193 + 3.333333334 = 5.024815264
x = 5.024815264

Simplifying
x = 5.024815264


Subproblem 2
x + -3.333333334 = -1.69148193

Simplifying
x + -3.333333334 = -1.69148193

Reorder the terms:
-3.333333334 + x = -1.69148193

Solving
-3.333333334 + x = -1.69148193

Solving for variable 'x'.

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

Add '3.333333334' to each side of the equation.
-3.333333334 + 3.333333334 + x = -1.69148193 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + x = -1.69148193 + 3.333333334
x = -1.69148193 + 3.333333334

Combine like terms: -1.69148193 + 3.333333334 = 1.641851404
x = 1.641851404

Simplifying
x = 1.641851404


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.024815264, 1.641851404}

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