(u+8)(u+8)-24=0

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Solution for (u+8)(u+8)-24=0 equation: 


Simplifying
(u + 8)(u + 8) + -24 = 0

Reorder the terms:
(8 + u)(u + 8) + -24 = 0

Reorder the terms:
(8 + u)(8 + u) + -24 = 0

Multiply (8 + u) * (8 + u)
(8(8 + u) + u(8 + u)) + -24 = 0
((8 * 8 + u * 8) + u(8 + u)) + -24 = 0
((64 + 8u) + u(8 + u)) + -24 = 0
(64 + 8u + (8 * u + u * u)) + -24 = 0
(64 + 8u + (8u + u2)) + -24 = 0

Combine like terms: 8u + 8u = 16u
(64 + 16u + u2) + -24 = 0

Reorder the terms:
64 + -24 + 16u + u2 = 0

Combine like terms: 64 + -24 = 40
40 + 16u + u2 = 0

Solving
40 + 16u + u2 = 0

Solving for variable 'u'.

Begin completing the square.

Move the constant term to the right:

Add '-40' to each side of the equation.
40 + 16u + -40 + u2 = 0 + -40

Reorder the terms:
40 + -40 + 16u + u2 = 0 + -40

Combine like terms: 40 + -40 = 0
0 + 16u + u2 = 0 + -40
16u + u2 = 0 + -40

Combine like terms: 0 + -40 = -40
16u + u2 = -40

The u term is 16u.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16u + 64 + u2 = -40 + 64

Reorder the terms:
64 + 16u + u2 = -40 + 64

Combine like terms: -40 + 64 = 24
64 + 16u + u2 = 24

Factor a perfect square on the left side:
(u + 8)(u + 8) = 24

Calculate the square root of the right side: 4.898979486

Break this problem into two subproblems by setting 
(u + 8) equal to 4.898979486 and -4.898979486.


Subproblem 1
u + 8 = 4.898979486

Simplifying
u + 8 = 4.898979486

Reorder the terms:
8 + u = 4.898979486

Solving
8 + u = 4.898979486

Solving for variable 'u'.

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

Add '-8' to each side of the equation.
8 + -8 + u = 4.898979486 + -8

Combine like terms: 8 + -8 = 0
0 + u = 4.898979486 + -8
u = 4.898979486 + -8

Combine like terms: 4.898979486 + -8 = -3.101020514
u = -3.101020514

Simplifying
u = -3.101020514


Subproblem 2
u + 8 = -4.898979486

Simplifying
u + 8 = -4.898979486

Reorder the terms:
8 + u = -4.898979486

Solving
8 + u = -4.898979486

Solving for variable 'u'.

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

Add '-8' to each side of the equation.
8 + -8 + u = -4.898979486 + -8

Combine like terms: 8 + -8 = 0
0 + u = -4.898979486 + -8
u = -4.898979486 + -8

Combine like terms: -4.898979486 + -8 = -12.898979486
u = -12.898979486

Simplifying
u = -12.898979486


Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {-3.101020514, -12.898979486}

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