-y^2+8y-5=0

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Solution for -y^2+8y-5=0 equation: 


Simplifying
-1y2 + 8y + -5 = 0

Reorder the terms:
-5 + 8y + -1y2 = 0

Solving
-5 + 8y + -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'.
5 + -8y + y2 = 0

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -8y + -5 + y2 = 0 + -5

Reorder the terms:
5 + -5 + -8y + y2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -8y + y2 = 0 + -5
-8y + y2 = 0 + -5

Combine like terms: 0 + -5 = -5
-8y + y2 = -5

The y term is -8y.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8y + 16 + y2 = -5 + 16

Reorder the terms:
16 + -8y + y2 = -5 + 16

Combine like terms: -5 + 16 = 11
16 + -8y + y2 = 11

Factor a perfect square on the left side:
(y + -4)(y + -4) = 11

Calculate the square root of the right side: 3.31662479

Break this problem into two subproblems by setting 
(y + -4) equal to 3.31662479 and -3.31662479.


Subproblem 1
y + -4 = 3.31662479

Simplifying
y + -4 = 3.31662479

Reorder the terms:
-4 + y = 3.31662479

Solving
-4 + y = 3.31662479

Solving for variable 'y'.

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

Add '4' to each side of the equation.
-4 + 4 + y = 3.31662479 + 4

Combine like terms: -4 + 4 = 0
0 + y = 3.31662479 + 4
y = 3.31662479 + 4

Combine like terms: 3.31662479 + 4 = 7.31662479
y = 7.31662479

Simplifying
y = 7.31662479


Subproblem 2
y + -4 = -3.31662479

Simplifying
y + -4 = -3.31662479

Reorder the terms:
-4 + y = -3.31662479

Solving
-4 + y = -3.31662479

Solving for variable 'y'.

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

Add '4' to each side of the equation.
-4 + 4 + y = -3.31662479 + 4

Combine like terms: -4 + 4 = 0
0 + y = -3.31662479 + 4
y = -3.31662479 + 4

Combine like terms: -3.31662479 + 4 = 0.68337521
y = 0.68337521

Simplifying
y = 0.68337521


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {7.31662479, 0.68337521}

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