-4u^2+33u-23=0

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Solution for -4u^2+33u-23=0 equation: 


Simplifying
-4u2 + 33u + -23 = 0

Reorder the terms:
-23 + 33u + -4u2 = 0

Solving
-23 + 33u + -4u2 = 0

Solving for variable 'u'.

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

Divide each side by '-4'.
5.75 + -8.25u + u2 = 0

Move the constant term to the right:

Add '-5.75' to each side of the equation.
5.75 + -8.25u + -5.75 + u2 = 0 + -5.75

Reorder the terms:
5.75 + -5.75 + -8.25u + u2 = 0 + -5.75

Combine like terms: 5.75 + -5.75 = 0.00
0.00 + -8.25u + u2 = 0 + -5.75
-8.25u + u2 = 0 + -5.75

Combine like terms: 0 + -5.75 = -5.75
-8.25u + u2 = -5.75

The u term is -8.25u.  Take half its coefficient (-4.125).
Square it (17.015625) and add it to both sides.

Add '17.015625' to each side of the equation.
-8.25u + 17.015625 + u2 = -5.75 + 17.015625

Reorder the terms:
17.015625 + -8.25u + u2 = -5.75 + 17.015625

Combine like terms: -5.75 + 17.015625 = 11.265625
17.015625 + -8.25u + u2 = 11.265625

Factor a perfect square on the left side:
(u + -4.125)(u + -4.125) = 11.265625

Calculate the square root of the right side: 3.356430396

Break this problem into two subproblems by setting 
(u + -4.125) equal to 3.356430396 and -3.356430396.


Subproblem 1
u + -4.125 = 3.356430396

Simplifying
u + -4.125 = 3.356430396

Reorder the terms:
-4.125 + u = 3.356430396

Solving
-4.125 + u = 3.356430396

Solving for variable 'u'.

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

Add '4.125' to each side of the equation.
-4.125 + 4.125 + u = 3.356430396 + 4.125

Combine like terms: -4.125 + 4.125 = 0.000
0.000 + u = 3.356430396 + 4.125
u = 3.356430396 + 4.125

Combine like terms: 3.356430396 + 4.125 = 7.481430396
u = 7.481430396

Simplifying
u = 7.481430396


Subproblem 2
u + -4.125 = -3.356430396

Simplifying
u + -4.125 = -3.356430396

Reorder the terms:
-4.125 + u = -3.356430396

Solving
-4.125 + u = -3.356430396

Solving for variable 'u'.

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

Add '4.125' to each side of the equation.
-4.125 + 4.125 + u = -3.356430396 + 4.125

Combine like terms: -4.125 + 4.125 = 0.000
0.000 + u = -3.356430396 + 4.125
u = -3.356430396 + 4.125

Combine like terms: -3.356430396 + 4.125 = 0.768569604
u = 0.768569604

Simplifying
u = 0.768569604


Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {7.481430396, 0.768569604}

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