y^2-12y-11=0

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Solution for y^2-12y-11=0 equation:


Simplifying
y2 + -12y + -11 = 0

Reorder the terms:
-11 + -12y + y2 = 0

Solving
-11 + -12y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + -12y + 11 + y2 = 0 + 11

Reorder the terms:
-11 + 11 + -12y + y2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -12y + y2 = 0 + 11
-12y + y2 = 0 + 11

Combine like terms: 0 + 11 = 11
-12y + y2 = 11

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

Add '36' to each side of the equation.
-12y + 36 + y2 = 11 + 36

Reorder the terms:
36 + -12y + y2 = 11 + 36

Combine like terms: 11 + 36 = 47
36 + -12y + y2 = 47

Factor a perfect square on the left side:
(y + -6)(y + -6) = 47

Calculate the square root of the right side: 6.8556546

Break this problem into two subproblems by setting 
(y + -6) equal to 6.8556546 and -6.8556546.

Subproblem 1

y + -6 = 6.8556546 Simplifying y + -6 = 6.8556546 Reorder the terms: -6 + y = 6.8556546 Solving -6 + y = 6.8556546 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + y = 6.8556546 + 6 Combine like terms: -6 + 6 = 0 0 + y = 6.8556546 + 6 y = 6.8556546 + 6 Combine like terms: 6.8556546 + 6 = 12.8556546 y = 12.8556546 Simplifying y = 12.8556546

Subproblem 2

y + -6 = -6.8556546 Simplifying y + -6 = -6.8556546 Reorder the terms: -6 + y = -6.8556546 Solving -6 + y = -6.8556546 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + y = -6.8556546 + 6 Combine like terms: -6 + 6 = 0 0 + y = -6.8556546 + 6 y = -6.8556546 + 6 Combine like terms: -6.8556546 + 6 = -0.8556546 y = -0.8556546 Simplifying y = -0.8556546

Solution

The solution to the problem is based on the solutions from the subproblems. y = {12.8556546, -0.8556546}

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