y^2-8y-10=0

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Solution for y^2-8y-10=0 equation: 


Simplifying
y2 + -8y + -10 = 0

Reorder the terms:
-10 + -8y + y2 = 0

Solving
-10 + -8y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + -8y + 10 + y2 = 0 + 10

Reorder the terms:
-10 + 10 + -8y + y2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -8y + y2 = 0 + 10
-8y + y2 = 0 + 10

Combine like terms: 0 + 10 = 10
-8y + y2 = 10

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 = 10 + 16

Reorder the terms:
16 + -8y + y2 = 10 + 16

Combine like terms: 10 + 16 = 26
16 + -8y + y2 = 26

Factor a perfect square on the left side:
(y + -4)(y + -4) = 26

Calculate the square root of the right side: 5.099019514

Break this problem into two subproblems by setting 
(y + -4) equal to 5.099019514 and -5.099019514.


Subproblem 1
y + -4 = 5.099019514

Simplifying
y + -4 = 5.099019514

Reorder the terms:
-4 + y = 5.099019514

Solving
-4 + y = 5.099019514

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 = 5.099019514 + 4

Combine like terms: -4 + 4 = 0
0 + y = 5.099019514 + 4
y = 5.099019514 + 4

Combine like terms: 5.099019514 + 4 = 9.099019514
y = 9.099019514

Simplifying
y = 9.099019514


Subproblem 2
y + -4 = -5.099019514

Simplifying
y + -4 = -5.099019514

Reorder the terms:
-4 + y = -5.099019514

Solving
-4 + y = -5.099019514

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 = -5.099019514 + 4

Combine like terms: -4 + 4 = 0
0 + y = -5.099019514 + 4
y = -5.099019514 + 4

Combine like terms: -5.099019514 + 4 = -1.099019514
y = -1.099019514

Simplifying
y = -1.099019514


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {9.099019514, -1.099019514}

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