u^2-17u-43=0

Solution for u^2-17u-43=0 equation:

Simplifying
u2 + -17u + -43 = 0

Reorder the terms:
-43 + -17u + u2 = 0

Solving
-43 + -17u + u2 = 0

Solving for variable 'u'.

Begin completing the square.

Move the constant term to the right:

Add '43' to each side of the equation.
-43 + -17u + 43 + u2 = 0 + 43

Reorder the terms:
-43 + 43 + -17u + u2 = 0 + 43

Combine like terms: -43 + 43 = 0
0 + -17u + u2 = 0 + 43
-17u + u2 = 0 + 43

Combine like terms: 0 + 43 = 43
-17u + u2 = 43

The u term is -17u.  Take half its coefficient (-8.5).
Square it (72.25) and add it to both sides.

Add '72.25' to each side of the equation.
-17u + 72.25 + u2 = 43 + 72.25

Reorder the terms:
72.25 + -17u + u2 = 43 + 72.25

Combine like terms: 43 + 72.25 = 115.25
72.25 + -17u + u2 = 115.25

Factor a perfect square on the left side:
(u + -8.5)(u + -8.5) = 115.25

Calculate the square root of the right side: 10.735455277

Break this problem into two subproblems by setting 
(u + -8.5) equal to 10.735455277 and -10.735455277.

Subproblem 1
u + -8.5 = 10.735455277

Simplifying
u + -8.5 = 10.735455277

Reorder the terms:
-8.5 + u = 10.735455277

Solving
-8.5 + u = 10.735455277

Solving for variable 'u'.

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

Add '8.5' to each side of the equation.
-8.5 + 8.5 + u = 10.735455277 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + u = 10.735455277 + 8.5
u = 10.735455277 + 8.5

Combine like terms: 10.735455277 + 8.5 = 19.235455277
u = 19.235455277

Simplifying
u = 19.235455277

Subproblem 2
u + -8.5 = -10.735455277

Simplifying
u + -8.5 = -10.735455277

Reorder the terms:
-8.5 + u = -10.735455277

Solving
-8.5 + u = -10.735455277

Solving for variable 'u'.

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

Add '8.5' to each side of the equation.
-8.5 + 8.5 + u = -10.735455277 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + u = -10.735455277 + 8.5
u = -10.735455277 + 8.5

Combine like terms: -10.735455277 + 8.5 = -2.235455277
u = -2.235455277

Simplifying
u = -2.235455277

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {19.235455277, -2.235455277}