4u^2-33u+13=0

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Solution for 4u^2-33u+13=0 equation: 


Simplifying
4u2 + -33u + 13 = 0

Reorder the terms:
13 + -33u + 4u2 = 0

Solving
13 + -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'.
3.25 + -8.25u + u2 = 0

Move the constant term to the right:

Add '-3.25' to each side of the equation.
3.25 + -8.25u + -3.25 + u2 = 0 + -3.25

Reorder the terms:
3.25 + -3.25 + -8.25u + u2 = 0 + -3.25

Combine like terms: 3.25 + -3.25 = 0.00
0.00 + -8.25u + u2 = 0 + -3.25
-8.25u + u2 = 0 + -3.25

Combine like terms: 0 + -3.25 = -3.25
-8.25u + u2 = -3.25

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 = -3.25 + 17.015625

Reorder the terms:
17.015625 + -8.25u + u2 = -3.25 + 17.015625

Combine like terms: -3.25 + 17.015625 = 13.765625
17.015625 + -8.25u + u2 = 13.765625

Factor a perfect square on the left side:
(u + -4.125)(u + -4.125) = 13.765625

Calculate the square root of the right side: 3.71020552

Break this problem into two subproblems by setting 
(u + -4.125) equal to 3.71020552 and -3.71020552.


Subproblem 1
u + -4.125 = 3.71020552

Simplifying
u + -4.125 = 3.71020552

Reorder the terms:
-4.125 + u = 3.71020552

Solving
-4.125 + u = 3.71020552

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 = 3.71020552 + 4.125

Combine like terms: -4.125 + 4.125 = 0.000
0.000 + u = 3.71020552 + 4.125
u = 3.71020552 + 4.125

Combine like terms: 3.71020552 + 4.125 = 7.83520552
u = 7.83520552

Simplifying
u = 7.83520552


Subproblem 2
u + -4.125 = -3.71020552

Simplifying
u + -4.125 = -3.71020552

Reorder the terms:
-4.125 + u = -3.71020552

Solving
-4.125 + u = -3.71020552

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 = -3.71020552 + 4.125

Combine like terms: -4.125 + 4.125 = 0.000
0.000 + u = -3.71020552 + 4.125
u = -3.71020552 + 4.125

Combine like terms: -3.71020552 + 4.125 = 0.41479448
u = 0.41479448

Simplifying
u = 0.41479448


Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {7.83520552, 0.41479448}

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