12x^2-88x+57=0

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Solution for 12x^2-88x+57=0 equation: 


Simplifying
12x2 + -88x + 57 = 0

Reorder the terms:
57 + -88x + 12x2 = 0

Solving
57 + -88x + 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'.
4.75 + -7.333333333x + x2 = 0

Move the constant term to the right:

Add '-4.75' to each side of the equation.
4.75 + -7.333333333x + -4.75 + x2 = 0 + -4.75

Reorder the terms:
4.75 + -4.75 + -7.333333333x + x2 = 0 + -4.75

Combine like terms: 4.75 + -4.75 = 0.00
0.00 + -7.333333333x + x2 = 0 + -4.75
-7.333333333x + x2 = 0 + -4.75

Combine like terms: 0 + -4.75 = -4.75
-7.333333333x + x2 = -4.75

The x term is -7.333333333x.  Take half its coefficient (-3.666666667).
Square it (13.44444445) and add it to both sides.

Add '13.44444445' to each side of the equation.
-7.333333333x + 13.44444445 + x2 = -4.75 + 13.44444445

Reorder the terms:
13.44444445 + -7.333333333x + x2 = -4.75 + 13.44444445

Combine like terms: -4.75 + 13.44444445 = 8.69444445
13.44444445 + -7.333333333x + x2 = 8.69444445

Factor a perfect square on the left side:
(x + -3.666666667)(x + -3.666666667) = 8.69444445

Calculate the square root of the right side: 2.948634336

Break this problem into two subproblems by setting 
(x + -3.666666667) equal to 2.948634336 and -2.948634336.


Subproblem 1
x + -3.666666667 = 2.948634336

Simplifying
x + -3.666666667 = 2.948634336

Reorder the terms:
-3.666666667 + x = 2.948634336

Solving
-3.666666667 + x = 2.948634336

Solving for variable 'x'.

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

Add '3.666666667' to each side of the equation.
-3.666666667 + 3.666666667 + x = 2.948634336 + 3.666666667

Combine like terms: -3.666666667 + 3.666666667 = 0.000000000
0.000000000 + x = 2.948634336 + 3.666666667
x = 2.948634336 + 3.666666667

Combine like terms: 2.948634336 + 3.666666667 = 6.615301003
x = 6.615301003

Simplifying
x = 6.615301003


Subproblem 2
x + -3.666666667 = -2.948634336

Simplifying
x + -3.666666667 = -2.948634336

Reorder the terms:
-3.666666667 + x = -2.948634336

Solving
-3.666666667 + x = -2.948634336

Solving for variable 'x'.

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

Add '3.666666667' to each side of the equation.
-3.666666667 + 3.666666667 + x = -2.948634336 + 3.666666667

Combine like terms: -3.666666667 + 3.666666667 = 0.000000000
0.000000000 + x = -2.948634336 + 3.666666667
x = -2.948634336 + 3.666666667

Combine like terms: -2.948634336 + 3.666666667 = 0.718032331
x = 0.718032331

Simplifying
x = 0.718032331


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.615301003, 0.718032331}

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