u^2+7u=-8

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Solution for u^2+7u=-8 equation: 


Simplifying
u2 + 7u = -8

Reorder the terms:
7u + u2 = -8

Solving
7u + u2 = -8

Solving for variable 'u'.

Reorder the terms:
8 + 7u + u2 = -8 + 8

Combine like terms: -8 + 8 = 0
8 + 7u + u2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + 7u + -8 + u2 = 0 + -8

Reorder the terms:
8 + -8 + 7u + u2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 7u + u2 = 0 + -8
7u + u2 = 0 + -8

Combine like terms: 0 + -8 = -8
7u + u2 = -8

The u term is 7u.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7u + 12.25 + u2 = -8 + 12.25

Reorder the terms:
12.25 + 7u + u2 = -8 + 12.25

Combine like terms: -8 + 12.25 = 4.25
12.25 + 7u + u2 = 4.25

Factor a perfect square on the left side:
(u + 3.5)(u + 3.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(u + 3.5) equal to 2.061552813 and -2.061552813.


Subproblem 1
u + 3.5 = 2.061552813

Simplifying
u + 3.5 = 2.061552813

Reorder the terms:
3.5 + u = 2.061552813

Solving
3.5 + u = 2.061552813

Solving for variable 'u'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + u = 2.061552813 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + u = 2.061552813 + -3.5
u = 2.061552813 + -3.5

Combine like terms: 2.061552813 + -3.5 = -1.438447187
u = -1.438447187

Simplifying
u = -1.438447187


Subproblem 2
u + 3.5 = -2.061552813

Simplifying
u + 3.5 = -2.061552813

Reorder the terms:
3.5 + u = -2.061552813

Solving
3.5 + u = -2.061552813

Solving for variable 'u'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + u = -2.061552813 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + u = -2.061552813 + -3.5
u = -2.061552813 + -3.5

Combine like terms: -2.061552813 + -3.5 = -5.561552813
u = -5.561552813

Simplifying
u = -5.561552813


Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {-1.438447187, -5.561552813}

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