-10=-2u(u+6)-9

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Solution for -10=-2u(u+6)-9 equation:


Simplifying
-10 = -2u(u + 6) + -9

Reorder the terms:
-10 = -2u(6 + u) + -9
-10 = (6 * -2u + u * -2u) + -9
-10 = (-12u + -2u2) + -9

Reorder the terms:
-10 = -9 + -12u + -2u2

Solving
-10 = -9 + -12u + -2u2

Solving for variable 'u'.

Combine like terms: -10 + 9 = -1
-1 + 12u + 2u2 = -9 + -12u + -2u2 + 9 + 12u + 2u2

Reorder the terms:
-1 + 12u + 2u2 = -9 + 9 + -12u + 12u + -2u2 + 2u2

Combine like terms: -9 + 9 = 0
-1 + 12u + 2u2 = 0 + -12u + 12u + -2u2 + 2u2
-1 + 12u + 2u2 = -12u + 12u + -2u2 + 2u2

Combine like terms: -12u + 12u = 0
-1 + 12u + 2u2 = 0 + -2u2 + 2u2
-1 + 12u + 2u2 = -2u2 + 2u2

Combine like terms: -2u2 + 2u2 = 0
-1 + 12u + 2u2 = 0

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

Divide each side by '2'.
-0.5 + 6u + u2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + 6u + 0.5 + u2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + 6u + u2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + 6u + u2 = 0 + 0.5
6u + u2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
6u + u2 = 0.5

The u term is 6u.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6u + 9 + u2 = 0.5 + 9

Reorder the terms:
9 + 6u + u2 = 0.5 + 9

Combine like terms: 0.5 + 9 = 9.5
9 + 6u + u2 = 9.5

Factor a perfect square on the left side:
(u + 3)(u + 3) = 9.5

Calculate the square root of the right side: 3.082207001

Break this problem into two subproblems by setting 
(u + 3) equal to 3.082207001 and -3.082207001.

Subproblem 1

u + 3 = 3.082207001 Simplifying u + 3 = 3.082207001 Reorder the terms: 3 + u = 3.082207001 Solving 3 + u = 3.082207001 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + u = 3.082207001 + -3 Combine like terms: 3 + -3 = 0 0 + u = 3.082207001 + -3 u = 3.082207001 + -3 Combine like terms: 3.082207001 + -3 = 0.082207001 u = 0.082207001 Simplifying u = 0.082207001

Subproblem 2

u + 3 = -3.082207001 Simplifying u + 3 = -3.082207001 Reorder the terms: 3 + u = -3.082207001 Solving 3 + u = -3.082207001 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + u = -3.082207001 + -3 Combine like terms: 3 + -3 = 0 0 + u = -3.082207001 + -3 u = -3.082207001 + -3 Combine like terms: -3.082207001 + -3 = -6.082207001 u = -6.082207001 Simplifying u = -6.082207001

Solution

The solution to the problem is based on the solutions from the subproblems. u = {0.082207001, -6.082207001}

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