u^2-12u+36+3=78

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Solution for u^2-12u+36+3=78 equation:


Simplifying
u2 + -12u + 36 + 3 = 78

Reorder the terms:
36 + 3 + -12u + u2 = 78

Combine like terms: 36 + 3 = 39
39 + -12u + u2 = 78

Solving
39 + -12u + u2 = 78

Solving for variable 'u'.

Reorder the terms:
39 + -78 + -12u + u2 = 78 + -78

Combine like terms: 39 + -78 = -39
-39 + -12u + u2 = 78 + -78

Combine like terms: 78 + -78 = 0
-39 + -12u + u2 = 0

Begin completing the square.

Move the constant term to the right:

Add '39' to each side of the equation.
-39 + -12u + 39 + u2 = 0 + 39

Reorder the terms:
-39 + 39 + -12u + u2 = 0 + 39

Combine like terms: -39 + 39 = 0
0 + -12u + u2 = 0 + 39
-12u + u2 = 0 + 39

Combine like terms: 0 + 39 = 39
-12u + u2 = 39

The u term is -12u.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12u + 36 + u2 = 39 + 36

Reorder the terms:
36 + -12u + u2 = 39 + 36

Combine like terms: 39 + 36 = 75
36 + -12u + u2 = 75

Factor a perfect square on the left side:
(u + -6)(u + -6) = 75

Calculate the square root of the right side: 8.660254038

Break this problem into two subproblems by setting 
(u + -6) equal to 8.660254038 and -8.660254038.

Subproblem 1

u + -6 = 8.660254038 Simplifying u + -6 = 8.660254038 Reorder the terms: -6 + u = 8.660254038 Solving -6 + u = 8.660254038 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + u = 8.660254038 + 6 Combine like terms: -6 + 6 = 0 0 + u = 8.660254038 + 6 u = 8.660254038 + 6 Combine like terms: 8.660254038 + 6 = 14.660254038 u = 14.660254038 Simplifying u = 14.660254038

Subproblem 2

u + -6 = -8.660254038 Simplifying u + -6 = -8.660254038 Reorder the terms: -6 + u = -8.660254038 Solving -6 + u = -8.660254038 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + u = -8.660254038 + 6 Combine like terms: -6 + 6 = 0 0 + u = -8.660254038 + 6 u = -8.660254038 + 6 Combine like terms: -8.660254038 + 6 = -2.660254038 u = -2.660254038 Simplifying u = -2.660254038

Solution

The solution to the problem is based on the solutions from the subproblems. u = {14.660254038, -2.660254038}

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