u^2+3u-14=0

Solution for u^2+3u-14=0 equation:

Simplifying
u2 + 3u + -14 = 0

Reorder the terms:
-14 + 3u + u2 = 0

Solving
-14 + 3u + u2 = 0

Solving for variable 'u'.

Begin completing the square.

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + 3u + 14 + u2 = 0 + 14

Reorder the terms:
-14 + 14 + 3u + u2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + 3u + u2 = 0 + 14
3u + u2 = 0 + 14

Combine like terms: 0 + 14 = 14
3u + u2 = 14

The u term is 3u.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3u + 2.25 + u2 = 14 + 2.25

Reorder the terms:
2.25 + 3u + u2 = 14 + 2.25

Combine like terms: 14 + 2.25 = 16.25
2.25 + 3u + u2 = 16.25

Factor a perfect square on the left side:
(u + 1.5)(u + 1.5) = 16.25

Calculate the square root of the right side: 4.031128874

Break this problem into two subproblems by setting 
(u + 1.5) equal to 4.031128874 and -4.031128874.

Subproblem 1
u + 1.5 = 4.031128874

Simplifying
u + 1.5 = 4.031128874

Reorder the terms:
1.5 + u = 4.031128874

Solving
1.5 + u = 4.031128874

Solving for variable 'u'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + u = 4.031128874 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + u = 4.031128874 + -1.5
u = 4.031128874 + -1.5

Combine like terms: 4.031128874 + -1.5 = 2.531128874
u = 2.531128874

Simplifying
u = 2.531128874

Subproblem 2
u + 1.5 = -4.031128874

Simplifying
u + 1.5 = -4.031128874

Reorder the terms:
1.5 + u = -4.031128874

Solving
1.5 + u = -4.031128874

Solving for variable 'u'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + u = -4.031128874 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + u = -4.031128874 + -1.5
u = -4.031128874 + -1.5

Combine like terms: -4.031128874 + -1.5 = -5.531128874
u = -5.531128874

Simplifying
u = -5.531128874

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {2.531128874, -5.531128874}