3x^2-25x+12=0

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Solution for 3x^2-25x+12=0 equation: 


Simplifying
3x2 + -25x + 12 = 0

Reorder the terms:
12 + -25x + 3x2 = 0

Solving
12 + -25x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
4 + -8.333333333x + x2 = 0

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -8.333333333x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + -8.333333333x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -8.333333333x + x2 = 0 + -4
-8.333333333x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
-8.333333333x + x2 = -4

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 = -4 + 17.36111111

Reorder the terms:
17.36111111 + -8.333333333x + x2 = -4 + 17.36111111

Combine like terms: -4 + 17.36111111 = 13.36111111
17.36111111 + -8.333333333x + x2 = 13.36111111

Factor a perfect square on the left side:
(x + -4.166666667)(x + -4.166666667) = 13.36111111

Calculate the square root of the right side: 3.655285366

Break this problem into two subproblems by setting 
(x + -4.166666667) equal to 3.655285366 and -3.655285366.


Subproblem 1
x + -4.166666667 = 3.655285366

Simplifying
x + -4.166666667 = 3.655285366

Reorder the terms:
-4.166666667 + x = 3.655285366

Solving
-4.166666667 + x = 3.655285366

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 = 3.655285366 + 4.166666667

Combine like terms: -4.166666667 + 4.166666667 = 0.000000000
0.000000000 + x = 3.655285366 + 4.166666667
x = 3.655285366 + 4.166666667

Combine like terms: 3.655285366 + 4.166666667 = 7.821952033
x = 7.821952033

Simplifying
x = 7.821952033


Subproblem 2
x + -4.166666667 = -3.655285366

Simplifying
x + -4.166666667 = -3.655285366

Reorder the terms:
-4.166666667 + x = -3.655285366

Solving
-4.166666667 + x = -3.655285366

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 = -3.655285366 + 4.166666667

Combine like terms: -4.166666667 + 4.166666667 = 0.000000000
0.000000000 + x = -3.655285366 + 4.166666667
x = -3.655285366 + 4.166666667

Combine like terms: -3.655285366 + 4.166666667 = 0.511381301
x = 0.511381301

Simplifying
x = 0.511381301


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.821952033, 0.511381301}

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