12x^2-75x+85.25=0

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Solution for 12x^2-75x+85.25=0 equation: 


Simplifying
12x2 + -75x + 85.25 = 0

Reorder the terms:
85.25 + -75x + 12x2 = 0

Solving
85.25 + -75x + 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'.
7.104166667 + -6.25x + x2 = 0

Move the constant term to the right:

Add '-7.104166667' to each side of the equation.
7.104166667 + -6.25x + -7.104166667 + x2 = 0 + -7.104166667

Reorder the terms:
7.104166667 + -7.104166667 + -6.25x + x2 = 0 + -7.104166667

Combine like terms: 7.104166667 + -7.104166667 = 0.000000000
0.000000000 + -6.25x + x2 = 0 + -7.104166667
-6.25x + x2 = 0 + -7.104166667

Combine like terms: 0 + -7.104166667 = -7.104166667
-6.25x + x2 = -7.104166667

The x term is -6.25x.  Take half its coefficient (-3.125).
Square it (9.765625) and add it to both sides.

Add '9.765625' to each side of the equation.
-6.25x + 9.765625 + x2 = -7.104166667 + 9.765625

Reorder the terms:
9.765625 + -6.25x + x2 = -7.104166667 + 9.765625

Combine like terms: -7.104166667 + 9.765625 = 2.661458333
9.765625 + -6.25x + x2 = 2.661458333

Factor a perfect square on the left side:
(x + -3.125)(x + -3.125) = 2.661458333

Calculate the square root of the right side: 1.631397662

Break this problem into two subproblems by setting 
(x + -3.125) equal to 1.631397662 and -1.631397662.


Subproblem 1
x + -3.125 = 1.631397662

Simplifying
x + -3.125 = 1.631397662

Reorder the terms:
-3.125 + x = 1.631397662

Solving
-3.125 + x = 1.631397662

Solving for variable 'x'.

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

Add '3.125' to each side of the equation.
-3.125 + 3.125 + x = 1.631397662 + 3.125

Combine like terms: -3.125 + 3.125 = 0.000
0.000 + x = 1.631397662 + 3.125
x = 1.631397662 + 3.125

Combine like terms: 1.631397662 + 3.125 = 4.756397662
x = 4.756397662

Simplifying
x = 4.756397662


Subproblem 2
x + -3.125 = -1.631397662

Simplifying
x + -3.125 = -1.631397662

Reorder the terms:
-3.125 + x = -1.631397662

Solving
-3.125 + x = -1.631397662

Solving for variable 'x'.

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

Add '3.125' to each side of the equation.
-3.125 + 3.125 + x = -1.631397662 + 3.125

Combine like terms: -3.125 + 3.125 = 0.000
0.000 + x = -1.631397662 + 3.125
x = -1.631397662 + 3.125

Combine like terms: -1.631397662 + 3.125 = 1.493602338
x = 1.493602338

Simplifying
x = 1.493602338


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.756397662, 1.493602338}

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