-8u^2+5329-u-5=0

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Solution for -8u^2+5329-u-5=0 equation:


Simplifying
-8u2 + 5329 + -1u + -5 = 0

Reorder the terms:
5329 + -5 + -1u + -8u2 = 0

Combine like terms: 5329 + -5 = 5324
5324 + -1u + -8u2 = 0

Solving
5324 + -1u + -8u2 = 0

Solving for variable 'u'.

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

Divide each side by '-8'.
-665.5 + 0.125u + u2 = 0

Move the constant term to the right:

Add '665.5' to each side of the equation.
-665.5 + 0.125u + 665.5 + u2 = 0 + 665.5

Reorder the terms:
-665.5 + 665.5 + 0.125u + u2 = 0 + 665.5

Combine like terms: -665.5 + 665.5 = 0.0
0.0 + 0.125u + u2 = 0 + 665.5
0.125u + u2 = 0 + 665.5

Combine like terms: 0 + 665.5 = 665.5
0.125u + u2 = 665.5

The u term is 0.125u.  Take half its coefficient (0.0625).
Square it (0.00390625) and add it to both sides.

Add '0.00390625' to each side of the equation.
0.125u + 0.00390625 + u2 = 665.5 + 0.00390625

Reorder the terms:
0.00390625 + 0.125u + u2 = 665.5 + 0.00390625

Combine like terms: 665.5 + 0.00390625 = 665.50390625
0.00390625 + 0.125u + u2 = 665.50390625

Factor a perfect square on the left side:
(u + 0.0625)(u + 0.0625) = 665.50390625

Calculate the square root of the right side: 25.797362389

Break this problem into two subproblems by setting 
(u + 0.0625) equal to 25.797362389 and -25.797362389.

Subproblem 1

u + 0.0625 = 25.797362389 Simplifying u + 0.0625 = 25.797362389 Reorder the terms: 0.0625 + u = 25.797362389 Solving 0.0625 + u = 25.797362389 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-0.0625' to each side of the equation. 0.0625 + -0.0625 + u = 25.797362389 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + u = 25.797362389 + -0.0625 u = 25.797362389 + -0.0625 Combine like terms: 25.797362389 + -0.0625 = 25.734862389 u = 25.734862389 Simplifying u = 25.734862389

Subproblem 2

u + 0.0625 = -25.797362389 Simplifying u + 0.0625 = -25.797362389 Reorder the terms: 0.0625 + u = -25.797362389 Solving 0.0625 + u = -25.797362389 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-0.0625' to each side of the equation. 0.0625 + -0.0625 + u = -25.797362389 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + u = -25.797362389 + -0.0625 u = -25.797362389 + -0.0625 Combine like terms: -25.797362389 + -0.0625 = -25.859862389 u = -25.859862389 Simplifying u = -25.859862389

Solution

The solution to the problem is based on the solutions from the subproblems. u = {25.734862389, -25.859862389}

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