-y^2+6y-1=0

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Solution for -y^2+6y-1=0 equation: 


Simplifying
-1y2 + 6y + -1 = 0

Reorder the terms:
-1 + 6y + -1y2 = 0

Solving
-1 + 6y + -1y2 = 0

Solving for variable 'y'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
1 + -6y + y2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -6y + -1 + y2 = 0 + -1

Reorder the terms:
1 + -1 + -6y + y2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -6y + y2 = 0 + -1
-6y + y2 = 0 + -1

Combine like terms: 0 + -1 = -1
-6y + y2 = -1

The y term is -6y.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6y + 9 + y2 = -1 + 9

Reorder the terms:
9 + -6y + y2 = -1 + 9

Combine like terms: -1 + 9 = 8
9 + -6y + y2 = 8

Factor a perfect square on the left side:
(y + -3)(y + -3) = 8

Calculate the square root of the right side: 2.828427125

Break this problem into two subproblems by setting 
(y + -3) equal to 2.828427125 and -2.828427125.


Subproblem 1
y + -3 = 2.828427125

Simplifying
y + -3 = 2.828427125

Reorder the terms:
-3 + y = 2.828427125

Solving
-3 + y = 2.828427125

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + 3 + y = 2.828427125 + 3

Combine like terms: -3 + 3 = 0
0 + y = 2.828427125 + 3
y = 2.828427125 + 3

Combine like terms: 2.828427125 + 3 = 5.828427125
y = 5.828427125

Simplifying
y = 5.828427125


Subproblem 2
y + -3 = -2.828427125

Simplifying
y + -3 = -2.828427125

Reorder the terms:
-3 + y = -2.828427125

Solving
-3 + y = -2.828427125

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + 3 + y = -2.828427125 + 3

Combine like terms: -3 + 3 = 0
0 + y = -2.828427125 + 3
y = -2.828427125 + 3

Combine like terms: -2.828427125 + 3 = 0.171572875
y = 0.171572875

Simplifying
y = 0.171572875


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {5.828427125, 0.171572875}

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