u^2-12u-15=0

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Solution for u^2-12u-15=0 equation:


Simplifying
u2 + -12u + -15 = 0

Reorder the terms:
-15 + -12u + u2 = 0

Solving
-15 + -12u + u2 = 0

Solving for variable 'u'.

Begin completing the square.

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + -12u + 15 + u2 = 0 + 15

Reorder the terms:
-15 + 15 + -12u + u2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -12u + u2 = 0 + 15
-12u + u2 = 0 + 15

Combine like terms: 0 + 15 = 15
-12u + u2 = 15

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 = 15 + 36

Reorder the terms:
36 + -12u + u2 = 15 + 36

Combine like terms: 15 + 36 = 51
36 + -12u + u2 = 51

Factor a perfect square on the left side:
(u + -6)(u + -6) = 51

Calculate the square root of the right side: 7.141428429

Break this problem into two subproblems by setting 
(u + -6) equal to 7.141428429 and -7.141428429.

Subproblem 1

u + -6 = 7.141428429 Simplifying u + -6 = 7.141428429 Reorder the terms: -6 + u = 7.141428429 Solving -6 + u = 7.141428429 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 = 7.141428429 + 6 Combine like terms: -6 + 6 = 0 0 + u = 7.141428429 + 6 u = 7.141428429 + 6 Combine like terms: 7.141428429 + 6 = 13.141428429 u = 13.141428429 Simplifying u = 13.141428429

Subproblem 2

u + -6 = -7.141428429 Simplifying u + -6 = -7.141428429 Reorder the terms: -6 + u = -7.141428429 Solving -6 + u = -7.141428429 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 = -7.141428429 + 6 Combine like terms: -6 + 6 = 0 0 + u = -7.141428429 + 6 u = -7.141428429 + 6 Combine like terms: -7.141428429 + 6 = -1.141428429 u = -1.141428429 Simplifying u = -1.141428429

Solution

The solution to the problem is based on the solutions from the subproblems. u = {13.141428429, -1.141428429}

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