u=4sqrt(-2)u^2-1

Solution for u=4sqrt(-2)u^2-1 equation:

Simplifying
u = 4sqrt(-2) * u2 + -1

Reorder the terms for easier multiplication:
u = 4 * -2qrst * u2 + -1

Multiply 4 * -2
u = -8qrst * u2 + -1

Multiply qrst * u2
u = -8qrstu2 + -1

Reorder the terms:
u = -1 + -8qrstu2

Solving
u = -1 + -8qrstu2

Solving for variable 'u'.

Reorder the terms:
1 + 8qrstu2 + u = -1 + -8qrstu2 + 1 + 8qrstu2

Reorder the terms:
1 + 8qrstu2 + u = -1 + 1 + -8qrstu2 + 8qrstu2

Combine like terms: -1 + 1 = 0
1 + 8qrstu2 + u = 0 + -8qrstu2 + 8qrstu2
1 + 8qrstu2 + u = -8qrstu2 + 8qrstu2

Combine like terms: -8qrstu2 + 8qrstu2 = 0
1 + 8qrstu2 + u = 0

Begin completing the square.  Divide all terms by
8qrst the coefficient of the squared term: 

Divide each side by '8qrst'.
0.125q-1r-1s-1t-1 + u2 + 0.125q-1r-1s-1t-1u = 0q-1r-1s-1t-1

Move the constant term to the right:

Add '-0.125' to each side of the equation.
0.125q-1r-1s-1t-1 + u2 + -0.125 + 0.125q-1r-1s-1t-1u = -0.125 + 0q-1r-1s-1t-1

Reorder the terms:
-0.125 + 0.125q-1r-1s-1t-1 + 0.125q-1r-1s-1t-1u + u2 = -0.125 + 0q-1r-1s-1t-1

Combine like terms: -0.125 + 0 = -0.125
-0.125 + 0.125q-1r-1s-1t-1 + 0.125q-1r-1s-1t-1u + u2 = -0.125

The u term is q-1r-1s-1t-1u.  Take half its coefficient (0.5q-1r-1s-1t-1).
Square it (0.25q-2r-2s-2t-2) and add it to both sides.

Add '0.25q-2r-2s-2t-2' to each side of the equation.
-0.125 + 0.125q-1r-1s-1t-1 + 0.125q-1r-1s-1t-1u + 0.25q-2r-2s-2t-2 + u2 = -0.125 + 0.25q-2r-2s-2t-2

Reorder the terms:
-0.125 + 0.25q-2r-2s-2t-2 + 0.125q-1r-1s-1t-1 + 0.125q-1r-1s-1t-1u + u2 = -0.125 + 0.25q-2r-2s-2t-2

Factor a perfect square on the left side:
(u + 0.5q-1r-1s-1t-1)(u + 0.5q-1r-1s-1t-1) = -0.125 + 0.25q-2r-2s-2t-2

Can't calculate square root of the right side.

The solution to this equation could not be determined.