3x^2-25x+36=0

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Solution for 3x^2-25x+36=0 equation: 


Simplifying
3x2 + -25x + 36 = 0

Reorder the terms:
36 + -25x + 3x2 = 0

Solving
36 + -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'.
12 + -8.333333333x + x2 = 0

Move the constant term to the right:

Add '-12' to each side of the equation.
12 + -8.333333333x + -12 + x2 = 0 + -12

Reorder the terms:
12 + -12 + -8.333333333x + x2 = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -8.333333333x + x2 = 0 + -12
-8.333333333x + x2 = 0 + -12

Combine like terms: 0 + -12 = -12
-8.333333333x + x2 = -12

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 + 17.36111111

Reorder the terms:
17.36111111 + -8.333333333x + x2 = -12 + 17.36111111

Combine like terms: -12 + 17.36111111 = 5.36111111
17.36111111 + -8.333333333x + x2 = 5.36111111

Factor a perfect square on the left side:
(x + -4.166666667)(x + -4.166666667) = 5.36111111

Calculate the square root of the right side: 2.315407331

Break this problem into two subproblems by setting 
(x + -4.166666667) equal to 2.315407331 and -2.315407331.


Subproblem 1
x + -4.166666667 = 2.315407331

Simplifying
x + -4.166666667 = 2.315407331

Reorder the terms:
-4.166666667 + x = 2.315407331

Solving
-4.166666667 + x = 2.315407331

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 = 2.315407331 + 4.166666667

Combine like terms: -4.166666667 + 4.166666667 = 0.000000000
0.000000000 + x = 2.315407331 + 4.166666667
x = 2.315407331 + 4.166666667

Combine like terms: 2.315407331 + 4.166666667 = 6.482073998
x = 6.482073998

Simplifying
x = 6.482073998


Subproblem 2
x + -4.166666667 = -2.315407331

Simplifying
x + -4.166666667 = -2.315407331

Reorder the terms:
-4.166666667 + x = -2.315407331

Solving
-4.166666667 + x = -2.315407331

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 = -2.315407331 + 4.166666667

Combine like terms: -4.166666667 + 4.166666667 = 0.000000000
0.000000000 + x = -2.315407331 + 4.166666667
x = -2.315407331 + 4.166666667

Combine like terms: -2.315407331 + 4.166666667 = 1.851259336
x = 1.851259336

Simplifying
x = 1.851259336


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.482073998, 1.851259336}

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