y^2-8y-7=0

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Solution for y^2-8y-7=0 equation: 


Simplifying
y2 + -8y + -7 = 0

Reorder the terms:
-7 + -8y + y2 = 0

Solving
-7 + -8y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + -8y + 7 + y2 = 0 + 7

Reorder the terms:
-7 + 7 + -8y + y2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -8y + y2 = 0 + 7
-8y + y2 = 0 + 7

Combine like terms: 0 + 7 = 7
-8y + y2 = 7

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 = 7 + 16

Reorder the terms:
16 + -8y + y2 = 7 + 16

Combine like terms: 7 + 16 = 23
16 + -8y + y2 = 23

Factor a perfect square on the left side:
(y + -4)(y + -4) = 23

Calculate the square root of the right side: 4.795831523

Break this problem into two subproblems by setting 
(y + -4) equal to 4.795831523 and -4.795831523.


Subproblem 1
y + -4 = 4.795831523

Simplifying
y + -4 = 4.795831523

Reorder the terms:
-4 + y = 4.795831523

Solving
-4 + y = 4.795831523

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 = 4.795831523 + 4

Combine like terms: -4 + 4 = 0
0 + y = 4.795831523 + 4
y = 4.795831523 + 4

Combine like terms: 4.795831523 + 4 = 8.795831523
y = 8.795831523

Simplifying
y = 8.795831523


Subproblem 2
y + -4 = -4.795831523

Simplifying
y + -4 = -4.795831523

Reorder the terms:
-4 + y = -4.795831523

Solving
-4 + y = -4.795831523

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 = -4.795831523 + 4

Combine like terms: -4 + 4 = 0
0 + y = -4.795831523 + 4
y = -4.795831523 + 4

Combine like terms: -4.795831523 + 4 = -0.795831523
y = -0.795831523

Simplifying
y = -0.795831523


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {8.795831523, -0.795831523}

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