u^2-12u=31

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Solution for u^2-12u=31 equation:


Simplifying
u2 + -12u = 31

Reorder the terms:
-12u + u2 = 31

Solving
-12u + u2 = 31

Solving for variable 'u'.

Reorder the terms:
-31 + -12u + u2 = 31 + -31

Combine like terms: 31 + -31 = 0
-31 + -12u + u2 = 0

Begin completing the square.

Move the constant term to the right:

Add '31' to each side of the equation.
-31 + -12u + 31 + u2 = 0 + 31

Reorder the terms:
-31 + 31 + -12u + u2 = 0 + 31

Combine like terms: -31 + 31 = 0
0 + -12u + u2 = 0 + 31
-12u + u2 = 0 + 31

Combine like terms: 0 + 31 = 31
-12u + u2 = 31

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 = 31 + 36

Reorder the terms:
36 + -12u + u2 = 31 + 36

Combine like terms: 31 + 36 = 67
36 + -12u + u2 = 67

Factor a perfect square on the left side:
(u + -6)(u + -6) = 67

Calculate the square root of the right side: 8.185352772

Break this problem into two subproblems by setting 
(u + -6) equal to 8.185352772 and -8.185352772.

Subproblem 1

u + -6 = 8.185352772 Simplifying u + -6 = 8.185352772 Reorder the terms: -6 + u = 8.185352772 Solving -6 + u = 8.185352772 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 = 8.185352772 + 6 Combine like terms: -6 + 6 = 0 0 + u = 8.185352772 + 6 u = 8.185352772 + 6 Combine like terms: 8.185352772 + 6 = 14.185352772 u = 14.185352772 Simplifying u = 14.185352772

Subproblem 2

u + -6 = -8.185352772 Simplifying u + -6 = -8.185352772 Reorder the terms: -6 + u = -8.185352772 Solving -6 + u = -8.185352772 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 = -8.185352772 + 6 Combine like terms: -6 + 6 = 0 0 + u = -8.185352772 + 6 u = -8.185352772 + 6 Combine like terms: -8.185352772 + 6 = -2.185352772 u = -2.185352772 Simplifying u = -2.185352772

Solution

The solution to the problem is based on the solutions from the subproblems. u = {14.185352772, -2.185352772}

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