12x^2+-100x+150=0

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Solution for 12x^2+-100x+150=0 equation: 


Simplifying
12x2 + -100x + 150 = 0

Reorder the terms:
150 + -100x + 12x2 = 0

Solving
150 + -100x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(75 + -50x + 6x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(75 + -50x + 6x2)' equal to zero and attempt to solve:

Simplifying
75 + -50x + 6x2 = 0

Solving
75 + -50x + 6x2 = 0

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

Divide each side by '6'.
12.5 + -8.333333333x + x2 = 0

Move the constant term to the right:

Add '-12.5' to each side of the equation.
12.5 + -8.333333333x + -12.5 + x2 = 0 + -12.5

Reorder the terms:
12.5 + -12.5 + -8.333333333x + x2 = 0 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + -8.333333333x + x2 = 0 + -12.5
-8.333333333x + x2 = 0 + -12.5

Combine like terms: 0 + -12.5 = -12.5
-8.333333333x + x2 = -12.5

The x term is -8.333333333x.  Take half its coefficient (-4.166666667).
Square it (17.36111111) and add it to both sides.

Add '17.36111111' to each side of the equation.
-8.333333333x + 17.36111111 + x2 = -12.5 + 17.36111111

Reorder the terms:
17.36111111 + -8.333333333x + x2 = -12.5 + 17.36111111

Combine like terms: -12.5 + 17.36111111 = 4.86111111
17.36111111 + -8.333333333x + x2 = 4.86111111

Factor a perfect square on the left side:
(x + -4.166666667)(x + -4.166666667) = 4.86111111

Calculate the square root of the right side: 2.204792759

Break this problem into two subproblems by setting 
(x + -4.166666667) equal to 2.204792759 and -2.204792759.


Subproblem 1
x + -4.166666667 = 2.204792759

Simplifying
x + -4.166666667 = 2.204792759

Reorder the terms:
-4.166666667 + x = 2.204792759

Solving
-4.166666667 + x = 2.204792759

Solving for variable 'x'.

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

Add '4.166666667' to each side of the equation.
-4.166666667 + 4.166666667 + x = 2.204792759 + 4.166666667

Combine like terms: -4.166666667 + 4.166666667 = 0.000000000
0.000000000 + x = 2.204792759 + 4.166666667
x = 2.204792759 + 4.166666667

Combine like terms: 2.204792759 + 4.166666667 = 6.371459426
x = 6.371459426

Simplifying
x = 6.371459426


Subproblem 2
x + -4.166666667 = -2.204792759

Simplifying
x + -4.166666667 = -2.204792759

Reorder the terms:
-4.166666667 + x = -2.204792759

Solving
-4.166666667 + x = -2.204792759

Solving for variable 'x'.

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

Add '4.166666667' to each side of the equation.
-4.166666667 + 4.166666667 + x = -2.204792759 + 4.166666667

Combine like terms: -4.166666667 + 4.166666667 = 0.000000000
0.000000000 + x = -2.204792759 + 4.166666667
x = -2.204792759 + 4.166666667

Combine like terms: -2.204792759 + 4.166666667 = 1.961873908
x = 1.961873908

Simplifying
x = 1.961873908


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.371459426, 1.961873908}
Solution
x = {6.371459426, 1.961873908}

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