4u^2+25u+31=0

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Solution for 4u^2+25u+31=0 equation: 


Simplifying
4u2 + 25u + 31 = 0

Reorder the terms:
31 + 25u + 4u2 = 0

Solving
31 + 25u + 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'.
7.75 + 6.25u + u2 = 0

Move the constant term to the right:

Add '-7.75' to each side of the equation.
7.75 + 6.25u + -7.75 + u2 = 0 + -7.75

Reorder the terms:
7.75 + -7.75 + 6.25u + u2 = 0 + -7.75

Combine like terms: 7.75 + -7.75 = 0.00
0.00 + 6.25u + u2 = 0 + -7.75
6.25u + u2 = 0 + -7.75

Combine like terms: 0 + -7.75 = -7.75
6.25u + u2 = -7.75

The u term is 6.25u.  Take half its coefficient (3.125).
Square it (9.765625) and add it to both sides.

Add '9.765625' to each side of the equation.
6.25u + 9.765625 + u2 = -7.75 + 9.765625

Reorder the terms:
9.765625 + 6.25u + u2 = -7.75 + 9.765625

Combine like terms: -7.75 + 9.765625 = 2.015625
9.765625 + 6.25u + u2 = 2.015625

Factor a perfect square on the left side:
(u + 3.125)(u + 3.125) = 2.015625

Calculate the square root of the right side: 1.419727086

Break this problem into two subproblems by setting 
(u + 3.125) equal to 1.419727086 and -1.419727086.


Subproblem 1
u + 3.125 = 1.419727086

Simplifying
u + 3.125 = 1.419727086

Reorder the terms:
3.125 + u = 1.419727086

Solving
3.125 + u = 1.419727086

Solving for variable 'u'.

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

Add '-3.125' to each side of the equation.
3.125 + -3.125 + u = 1.419727086 + -3.125

Combine like terms: 3.125 + -3.125 = 0.000
0.000 + u = 1.419727086 + -3.125
u = 1.419727086 + -3.125

Combine like terms: 1.419727086 + -3.125 = -1.705272914
u = -1.705272914

Simplifying
u = -1.705272914


Subproblem 2
u + 3.125 = -1.419727086

Simplifying
u + 3.125 = -1.419727086

Reorder the terms:
3.125 + u = -1.419727086

Solving
3.125 + u = -1.419727086

Solving for variable 'u'.

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

Add '-3.125' to each side of the equation.
3.125 + -3.125 + u = -1.419727086 + -3.125

Combine like terms: 3.125 + -3.125 = 0.000
0.000 + u = -1.419727086 + -3.125
u = -1.419727086 + -3.125

Combine like terms: -1.419727086 + -3.125 = -4.544727086
u = -4.544727086

Simplifying
u = -4.544727086


Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {-1.705272914, -4.544727086}

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