u^2-5u-35=0

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Solution for u^2-5u-35=0 equation: 


Simplifying
u2 + -5u + -35 = 0

Reorder the terms:
-35 + -5u + u2 = 0

Solving
-35 + -5u + u2 = 0

Solving for variable 'u'.

Begin completing the square.

Move the constant term to the right:

Add '35' to each side of the equation.
-35 + -5u + 35 + u2 = 0 + 35

Reorder the terms:
-35 + 35 + -5u + u2 = 0 + 35

Combine like terms: -35 + 35 = 0
0 + -5u + u2 = 0 + 35
-5u + u2 = 0 + 35

Combine like terms: 0 + 35 = 35
-5u + u2 = 35

The u term is -5u.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5u + 6.25 + u2 = 35 + 6.25

Reorder the terms:
6.25 + -5u + u2 = 35 + 6.25

Combine like terms: 35 + 6.25 = 41.25
6.25 + -5u + u2 = 41.25

Factor a perfect square on the left side:
(u + -2.5)(u + -2.5) = 41.25

Calculate the square root of the right side: 6.422616289

Break this problem into two subproblems by setting 
(u + -2.5) equal to 6.422616289 and -6.422616289.


Subproblem 1
u + -2.5 = 6.422616289

Simplifying
u + -2.5 = 6.422616289

Reorder the terms:
-2.5 + u = 6.422616289

Solving
-2.5 + u = 6.422616289

Solving for variable 'u'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + u = 6.422616289 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + u = 6.422616289 + 2.5
u = 6.422616289 + 2.5

Combine like terms: 6.422616289 + 2.5 = 8.922616289
u = 8.922616289

Simplifying
u = 8.922616289


Subproblem 2
u + -2.5 = -6.422616289

Simplifying
u + -2.5 = -6.422616289

Reorder the terms:
-2.5 + u = -6.422616289

Solving
-2.5 + u = -6.422616289

Solving for variable 'u'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + u = -6.422616289 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + u = -6.422616289 + 2.5
u = -6.422616289 + 2.5

Combine like terms: -6.422616289 + 2.5 = -3.922616289
u = -3.922616289

Simplifying
u = -3.922616289


Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {8.922616289, -3.922616289}

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