y^2+13-8y=0

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Solution for y^2+13-8y=0 equation: 


Simplifying
y2 + 13 + -8y = 0

Reorder the terms:
13 + -8y + y2 = 0

Solving
13 + -8y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-13' to each side of the equation.
13 + -8y + -13 + y2 = 0 + -13

Reorder the terms:
13 + -13 + -8y + y2 = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -8y + y2 = 0 + -13
-8y + y2 = 0 + -13

Combine like terms: 0 + -13 = -13
-8y + y2 = -13

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 = -13 + 16

Reorder the terms:
16 + -8y + y2 = -13 + 16

Combine like terms: -13 + 16 = 3
16 + -8y + y2 = 3

Factor a perfect square on the left side:
(y + -4)(y + -4) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(y + -4) equal to 1.732050808 and -1.732050808.


Subproblem 1
y + -4 = 1.732050808

Simplifying
y + -4 = 1.732050808

Reorder the terms:
-4 + y = 1.732050808

Solving
-4 + y = 1.732050808

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 = 1.732050808 + 4

Combine like terms: -4 + 4 = 0
0 + y = 1.732050808 + 4
y = 1.732050808 + 4

Combine like terms: 1.732050808 + 4 = 5.732050808
y = 5.732050808

Simplifying
y = 5.732050808


Subproblem 2
y + -4 = -1.732050808

Simplifying
y + -4 = -1.732050808

Reorder the terms:
-4 + y = -1.732050808

Solving
-4 + y = -1.732050808

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 = -1.732050808 + 4

Combine like terms: -4 + 4 = 0
0 + y = -1.732050808 + 4
y = -1.732050808 + 4

Combine like terms: -1.732050808 + 4 = 2.267949192
y = 2.267949192

Simplifying
y = 2.267949192


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {5.732050808, 2.267949192}

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