-4x^2+31x-33=0

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Solution for -4x^2+31x-33=0 equation: 


Simplifying
-4x2 + 31x + -33 = 0

Reorder the terms:
-33 + 31x + -4x2 = 0

Solving
-33 + 31x + -4x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
8.25 + -7.75x + x2 = 0

Move the constant term to the right:

Add '-8.25' to each side of the equation.
8.25 + -7.75x + -8.25 + x2 = 0 + -8.25

Reorder the terms:
8.25 + -8.25 + -7.75x + x2 = 0 + -8.25

Combine like terms: 8.25 + -8.25 = 0.00
0.00 + -7.75x + x2 = 0 + -8.25
-7.75x + x2 = 0 + -8.25

Combine like terms: 0 + -8.25 = -8.25
-7.75x + x2 = -8.25

The x term is -7.75x.  Take half its coefficient (-3.875).
Square it (15.015625) and add it to both sides.

Add '15.015625' to each side of the equation.
-7.75x + 15.015625 + x2 = -8.25 + 15.015625

Reorder the terms:
15.015625 + -7.75x + x2 = -8.25 + 15.015625

Combine like terms: -8.25 + 15.015625 = 6.765625
15.015625 + -7.75x + x2 = 6.765625

Factor a perfect square on the left side:
(x + -3.875)(x + -3.875) = 6.765625

Calculate the square root of the right side: 2.601081506

Break this problem into two subproblems by setting 
(x + -3.875) equal to 2.601081506 and -2.601081506.


Subproblem 1
x + -3.875 = 2.601081506

Simplifying
x + -3.875 = 2.601081506

Reorder the terms:
-3.875 + x = 2.601081506

Solving
-3.875 + x = 2.601081506

Solving for variable 'x'.

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

Add '3.875' to each side of the equation.
-3.875 + 3.875 + x = 2.601081506 + 3.875

Combine like terms: -3.875 + 3.875 = 0.000
0.000 + x = 2.601081506 + 3.875
x = 2.601081506 + 3.875

Combine like terms: 2.601081506 + 3.875 = 6.476081506
x = 6.476081506

Simplifying
x = 6.476081506


Subproblem 2
x + -3.875 = -2.601081506

Simplifying
x + -3.875 = -2.601081506

Reorder the terms:
-3.875 + x = -2.601081506

Solving
-3.875 + x = -2.601081506

Solving for variable 'x'.

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

Add '3.875' to each side of the equation.
-3.875 + 3.875 + x = -2.601081506 + 3.875

Combine like terms: -3.875 + 3.875 = 0.000
0.000 + x = -2.601081506 + 3.875
x = -2.601081506 + 3.875

Combine like terms: -2.601081506 + 3.875 = 1.273918494
x = 1.273918494

Simplifying
x = 1.273918494


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.476081506, 1.273918494}

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