u^2-9.90u=44.55

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Solution for u^2-9.90u=44.55 equation: 


Simplifying
u2 + -9.90u = 44.55

Reorder the terms:
-9.90u + u2 = 44.55

Solving
-9.90u + u2 = 44.55

Solving for variable 'u'.

Reorder the terms:
-44.55 + -9.90u + u2 = 44.55 + -44.55

Combine like terms: 44.55 + -44.55 = 0.00
-44.55 + -9.90u + u2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '44.55' to each side of the equation.
-44.55 + -9.90u + 44.55 + u2 = 0.00 + 44.55

Reorder the terms:
-44.55 + 44.55 + -9.90u + u2 = 0.00 + 44.55

Combine like terms: -44.55 + 44.55 = 0.00
0.00 + -9.90u + u2 = 0.00 + 44.55
-9.90u + u2 = 0.00 + 44.55

Combine like terms: 0.00 + 44.55 = 44.55
-9.90u + u2 = 44.55

The u term is -9.90u.  Take half its coefficient (-4.95).
Square it (24.5025) and add it to both sides.

Add '24.5025' to each side of the equation.
-9.90u + 24.5025 + u2 = 44.55 + 24.5025

Reorder the terms:
24.5025 + -9.90u + u2 = 44.55 + 24.5025

Combine like terms: 44.55 + 24.5025 = 69.0525
24.5025 + -9.90u + u2 = 69.0525

Factor a perfect square on the left side:
(u + -4.95)(u + -4.95) = 69.0525

Calculate the square root of the right side: 8.309783391

Break this problem into two subproblems by setting 
(u + -4.95) equal to 8.309783391 and -8.309783391.


Subproblem 1
u + -4.95 = 8.309783391

Simplifying
u + -4.95 = 8.309783391

Reorder the terms:
-4.95 + u = 8.309783391

Solving
-4.95 + u = 8.309783391

Solving for variable 'u'.

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

Add '4.95' to each side of the equation.
-4.95 + 4.95 + u = 8.309783391 + 4.95

Combine like terms: -4.95 + 4.95 = 0.00
0.00 + u = 8.309783391 + 4.95
u = 8.309783391 + 4.95

Combine like terms: 8.309783391 + 4.95 = 13.259783391
u = 13.259783391

Simplifying
u = 13.259783391


Subproblem 2
u + -4.95 = -8.309783391

Simplifying
u + -4.95 = -8.309783391

Reorder the terms:
-4.95 + u = -8.309783391

Solving
-4.95 + u = -8.309783391

Solving for variable 'u'.

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

Add '4.95' to each side of the equation.
-4.95 + 4.95 + u = -8.309783391 + 4.95

Combine like terms: -4.95 + 4.95 = 0.00
0.00 + u = -8.309783391 + 4.95
u = -8.309783391 + 4.95

Combine like terms: -8.309783391 + 4.95 = -3.359783391
u = -3.359783391

Simplifying
u = -3.359783391


Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {13.259783391, -3.359783391}

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