-2u^2-7u-4=0

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Solution for -2u^2-7u-4=0 equation: 


Simplifying
-2u2 + -7u + -4 = 0

Reorder the terms:
-4 + -7u + -2u2 = 0

Solving
-4 + -7u + -2u2 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(4 + 7u + 2u2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(4 + 7u + 2u2)' equal to zero and attempt to solve:

Simplifying
4 + 7u + 2u2 = 0

Solving
4 + 7u + 2u2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
2 + 3.5u + u2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 3.5u + -2 + u2 = 0 + -2

Reorder the terms:
2 + -2 + 3.5u + u2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3.5u + u2 = 0 + -2
3.5u + u2 = 0 + -2

Combine like terms: 0 + -2 = -2
3.5u + u2 = -2

The u term is 3.5u.  Take half its coefficient (1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
3.5u + 3.0625 + u2 = -2 + 3.0625

Reorder the terms:
3.0625 + 3.5u + u2 = -2 + 3.0625

Combine like terms: -2 + 3.0625 = 1.0625
3.0625 + 3.5u + u2 = 1.0625

Factor a perfect square on the left side:
(u + 1.75)(u + 1.75) = 1.0625

Calculate the square root of the right side: 1.030776406

Break this problem into two subproblems by setting 
(u + 1.75) equal to 1.030776406 and -1.030776406.


Subproblem 1
u + 1.75 = 1.030776406

Simplifying
u + 1.75 = 1.030776406

Reorder the terms:
1.75 + u = 1.030776406

Solving
1.75 + u = 1.030776406

Solving for variable 'u'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + u = 1.030776406 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + u = 1.030776406 + -1.75
u = 1.030776406 + -1.75

Combine like terms: 1.030776406 + -1.75 = -0.719223594
u = -0.719223594

Simplifying
u = -0.719223594


Subproblem 2
u + 1.75 = -1.030776406

Simplifying
u + 1.75 = -1.030776406

Reorder the terms:
1.75 + u = -1.030776406

Solving
1.75 + u = -1.030776406

Solving for variable 'u'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + u = -1.030776406 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + u = -1.030776406 + -1.75
u = -1.030776406 + -1.75

Combine like terms: -1.030776406 + -1.75 = -2.780776406
u = -2.780776406

Simplifying
u = -2.780776406


Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {-0.719223594, -2.780776406}
Solution
u = {-0.719223594, -2.780776406}

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