u^2-12u+7=0

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Solution for u^2-12u+7=0 equation:


Simplifying
u2 + -12u + 7 = 0

Reorder the terms:
7 + -12u + u2 = 0

Solving
7 + -12u + u2 = 0

Solving for variable 'u'.

Begin completing the square.

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + -12u + -7 + u2 = 0 + -7

Reorder the terms:
7 + -7 + -12u + u2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -12u + u2 = 0 + -7
-12u + u2 = 0 + -7

Combine like terms: 0 + -7 = -7
-12u + u2 = -7

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 = -7 + 36

Reorder the terms:
36 + -12u + u2 = -7 + 36

Combine like terms: -7 + 36 = 29
36 + -12u + u2 = 29

Factor a perfect square on the left side:
(u + -6)(u + -6) = 29

Calculate the square root of the right side: 5.385164807

Break this problem into two subproblems by setting 
(u + -6) equal to 5.385164807 and -5.385164807.

Subproblem 1

u + -6 = 5.385164807 Simplifying u + -6 = 5.385164807 Reorder the terms: -6 + u = 5.385164807 Solving -6 + u = 5.385164807 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 = 5.385164807 + 6 Combine like terms: -6 + 6 = 0 0 + u = 5.385164807 + 6 u = 5.385164807 + 6 Combine like terms: 5.385164807 + 6 = 11.385164807 u = 11.385164807 Simplifying u = 11.385164807

Subproblem 2

u + -6 = -5.385164807 Simplifying u + -6 = -5.385164807 Reorder the terms: -6 + u = -5.385164807 Solving -6 + u = -5.385164807 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 = -5.385164807 + 6 Combine like terms: -6 + 6 = 0 0 + u = -5.385164807 + 6 u = -5.385164807 + 6 Combine like terms: -5.385164807 + 6 = 0.614835193 u = 0.614835193 Simplifying u = 0.614835193

Solution

The solution to the problem is based on the solutions from the subproblems. u = {11.385164807, 0.614835193}

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