u=64u^2-49

Solution for u=64u^2-49 equation:

Simplifying
u = 64u2 + -49

Reorder the terms:
u = -49 + 64u2

Solving
u = -49 + 64u2

Solving for variable 'u'.

Reorder the terms:
49 + u + -64u2 = -49 + 64u2 + 49 + -64u2

Reorder the terms:
49 + u + -64u2 = -49 + 49 + 64u2 + -64u2

Combine like terms: -49 + 49 = 0
49 + u + -64u2 = 0 + 64u2 + -64u2
49 + u + -64u2 = 64u2 + -64u2

Combine like terms: 64u2 + -64u2 = 0
49 + u + -64u2 = 0

Begin completing the square.  Divide all terms by
-64 the coefficient of the squared term: 

Divide each side by '-64'.
-0.765625 + -0.015625u + u2 = 0

Move the constant term to the right:

Add '0.765625' to each side of the equation.
-0.765625 + -0.015625u + 0.765625 + u2 = 0 + 0.765625

Reorder the terms:
-0.765625 + 0.765625 + -0.015625u + u2 = 0 + 0.765625

Combine like terms: -0.765625 + 0.765625 = 0.000000
0.000000 + -0.015625u + u2 = 0 + 0.765625
-0.015625u + u2 = 0 + 0.765625

Combine like terms: 0 + 0.765625 = 0.765625
-0.015625u + u2 = 0.765625

The u term is u.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-0.015625u + 0.25 + u2 = 0.765625 + 0.25

Reorder the terms:
0.25 + -0.015625u + u2 = 0.765625 + 0.25

Combine like terms: 0.765625 + 0.25 = 1.015625
0.25 + -0.015625u + u2 = 1.015625

Factor a perfect square on the left side:
(u + 0.5)(u + 0.5) = 1.015625

Calculate the square root of the right side: 1.007782219

Break this problem into two subproblems by setting 
(u + 0.5) equal to 1.007782219 and -1.007782219.

Subproblem 1
u + 0.5 = 1.007782219

Simplifying
u + 0.5 = 1.007782219

Reorder the terms:
0.5 + u = 1.007782219

Solving
0.5 + u = 1.007782219

Solving for variable 'u'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + u = 1.007782219 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + u = 1.007782219 + -0.5
u = 1.007782219 + -0.5

Combine like terms: 1.007782219 + -0.5 = 0.507782219
u = 0.507782219

Simplifying
u = 0.507782219

Subproblem 2
u + 0.5 = -1.007782219

Simplifying
u + 0.5 = -1.007782219

Reorder the terms:
0.5 + u = -1.007782219

Solving
0.5 + u = -1.007782219

Solving for variable 'u'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + u = -1.007782219 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + u = -1.007782219 + -0.5
u = -1.007782219 + -0.5

Combine like terms: -1.007782219 + -0.5 = -1.507782219
u = -1.507782219

Simplifying
u = -1.507782219

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {0.507782219, -1.507782219}