u^2-20u-33=0

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Solution for u^2-20u-33=0 equation:


Simplifying
u2 + -20u + -33 = 0

Reorder the terms:
-33 + -20u + u2 = 0

Solving
-33 + -20u + u2 = 0

Solving for variable 'u'.

Begin completing the square.

Move the constant term to the right:

Add '33' to each side of the equation.
-33 + -20u + 33 + u2 = 0 + 33

Reorder the terms:
-33 + 33 + -20u + u2 = 0 + 33

Combine like terms: -33 + 33 = 0
0 + -20u + u2 = 0 + 33
-20u + u2 = 0 + 33

Combine like terms: 0 + 33 = 33
-20u + u2 = 33

The u term is -20u.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20u + 100 + u2 = 33 + 100

Reorder the terms:
100 + -20u + u2 = 33 + 100

Combine like terms: 33 + 100 = 133
100 + -20u + u2 = 133

Factor a perfect square on the left side:
(u + -10)(u + -10) = 133

Calculate the square root of the right side: 11.532562595

Break this problem into two subproblems by setting 
(u + -10) equal to 11.532562595 and -11.532562595.


Subproblem 1
u + -10 = 11.532562595

Simplifying
u + -10 = 11.532562595

Reorder the terms:
-10 + u = 11.532562595

Solving
-10 + u = 11.532562595

Solving for variable 'u'.

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

Add '10' to each side of the equation.
-10 + 10 + u = 11.532562595 + 10

Combine like terms: -10 + 10 = 0
0 + u = 11.532562595 + 10
u = 11.532562595 + 10

Combine like terms: 11.532562595 + 10 = 21.532562595
u = 21.532562595

Simplifying
u = 21.532562595


Subproblem 2
u + -10 = -11.532562595

Simplifying
u + -10 = -11.532562595

Reorder the terms:
-10 + u = -11.532562595

Solving
-10 + u = -11.532562595

Solving for variable 'u'.

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

Add '10' to each side of the equation.
-10 + 10 + u = -11.532562595 + 10

Combine like terms: -10 + 10 = 0
0 + u = -11.532562595 + 10
u = -11.532562595 + 10

Combine like terms: -11.532562595 + 10 = -1.532562595
u = -1.532562595

Simplifying
u = -1.532562595


Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {21.532562595, -1.532562595}

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