2u^2+7u-64=0

Solution for 2u^2+7u-64=0 equation:

Simplifying
2u2 + 7u + -64 = 0

Reorder the terms:
-64 + 7u + 2u2 = 0

Solving
-64 + 7u + 2u2 = 0

Solving for variable 'u'.

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

Divide each side by '2'.
-32 + 3.5u + u2 = 0

Move the constant term to the right:

Add '32' to each side of the equation.
-32 + 3.5u + 32 + u2 = 0 + 32

Reorder the terms:
-32 + 32 + 3.5u + u2 = 0 + 32

Combine like terms: -32 + 32 = 0
0 + 3.5u + u2 = 0 + 32
3.5u + u2 = 0 + 32

Combine like terms: 0 + 32 = 32
3.5u + u2 = 32

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 = 32 + 3.0625

Reorder the terms:
3.0625 + 3.5u + u2 = 32 + 3.0625

Combine like terms: 32 + 3.0625 = 35.0625
3.0625 + 3.5u + u2 = 35.0625

Factor a perfect square on the left side:
(u + 1.75)(u + 1.75) = 35.0625

Calculate the square root of the right side: 5.921359641

Break this problem into two subproblems by setting 
(u + 1.75) equal to 5.921359641 and -5.921359641.

Subproblem 1
u + 1.75 = 5.921359641

Simplifying
u + 1.75 = 5.921359641

Reorder the terms:
1.75 + u = 5.921359641

Solving
1.75 + u = 5.921359641

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 = 5.921359641 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + u = 5.921359641 + -1.75
u = 5.921359641 + -1.75

Combine like terms: 5.921359641 + -1.75 = 4.171359641
u = 4.171359641

Simplifying
u = 4.171359641

Subproblem 2
u + 1.75 = -5.921359641

Simplifying
u + 1.75 = -5.921359641

Reorder the terms:
1.75 + u = -5.921359641

Solving
1.75 + u = -5.921359641

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 = -5.921359641 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + u = -5.921359641 + -1.75
u = -5.921359641 + -1.75

Combine like terms: -5.921359641 + -1.75 = -7.671359641
u = -7.671359641

Simplifying
u = -7.671359641

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {4.171359641, -7.671359641}