u(u-0.25)=0.0378

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Solution for u(u-0.25)=0.0378 equation: 


Simplifying
u(u + -0.25) = 0.0378

Reorder the terms:
u(-0.25 + u) = 0.0378
(-0.25 * u + u * u) = 0.0378
(-0.25u + u2) = 0.0378

Solving
-0.25u + u2 = 0.0378

Solving for variable 'u'.

Reorder the terms:
-0.0378 + -0.25u + u2 = 0.0378 + -0.0378

Combine like terms: 0.0378 + -0.0378 = 0.0000
-0.0378 + -0.25u + u2 = 0.0000

Begin completing the square.

Move the constant term to the right:

Add '0.0378' to each side of the equation.
-0.0378 + -0.25u + 0.0378 + u2 = 0.0000 + 0.0378

Reorder the terms:
-0.0378 + 0.0378 + -0.25u + u2 = 0.0000 + 0.0378

Combine like terms: -0.0378 + 0.0378 = 0.0000
0.0000 + -0.25u + u2 = 0.0000 + 0.0378
-0.25u + u2 = 0.0000 + 0.0378

Combine like terms: 0.0000 + 0.0378 = 0.0378
-0.25u + u2 = 0.0378

The u term is -0.25u.  Take half its coefficient (-0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
-0.25u + 0.015625 + u2 = 0.0378 + 0.015625

Reorder the terms:
0.015625 + -0.25u + u2 = 0.0378 + 0.015625

Combine like terms: 0.0378 + 0.015625 = 0.053425
0.015625 + -0.25u + u2 = 0.053425

Factor a perfect square on the left side:
(u + -0.125)(u + -0.125) = 0.053425

Calculate the square root of the right side: 0.231138487

Break this problem into two subproblems by setting 
(u + -0.125) equal to 0.231138487 and -0.231138487.


Subproblem 1
u + -0.125 = 0.231138487

Simplifying
u + -0.125 = 0.231138487

Reorder the terms:
-0.125 + u = 0.231138487

Solving
-0.125 + u = 0.231138487

Solving for variable 'u'.

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

Add '0.125' to each side of the equation.
-0.125 + 0.125 + u = 0.231138487 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + u = 0.231138487 + 0.125
u = 0.231138487 + 0.125

Combine like terms: 0.231138487 + 0.125 = 0.356138487
u = 0.356138487

Simplifying
u = 0.356138487


Subproblem 2
u + -0.125 = -0.231138487

Simplifying
u + -0.125 = -0.231138487

Reorder the terms:
-0.125 + u = -0.231138487

Solving
-0.125 + u = -0.231138487

Solving for variable 'u'.

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

Add '0.125' to each side of the equation.
-0.125 + 0.125 + u = -0.231138487 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + u = -0.231138487 + 0.125
u = -0.231138487 + 0.125

Combine like terms: -0.231138487 + 0.125 = -0.106138487
u = -0.106138487

Simplifying
u = -0.106138487


Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {0.356138487, -0.106138487}

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