y^2-10y-7=0

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Solution for y^2-10y-7=0 equation: 


Simplifying
y2 + -10y + -7 = 0

Reorder the terms:
-7 + -10y + y2 = 0

Solving
-7 + -10y + 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 + -10y + 7 + y2 = 0 + 7

Reorder the terms:
-7 + 7 + -10y + y2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -10y + y2 = 0 + 7
-10y + y2 = 0 + 7

Combine like terms: 0 + 7 = 7
-10y + y2 = 7

The y term is -10y.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10y + 25 + y2 = 7 + 25

Reorder the terms:
25 + -10y + y2 = 7 + 25

Combine like terms: 7 + 25 = 32
25 + -10y + y2 = 32

Factor a perfect square on the left side:
(y + -5)(y + -5) = 32

Calculate the square root of the right side: 5.656854249

Break this problem into two subproblems by setting 
(y + -5) equal to 5.656854249 and -5.656854249.


Subproblem 1
y + -5 = 5.656854249

Simplifying
y + -5 = 5.656854249

Reorder the terms:
-5 + y = 5.656854249

Solving
-5 + y = 5.656854249

Solving for variable 'y'.

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

Add '5' to each side of the equation.
-5 + 5 + y = 5.656854249 + 5

Combine like terms: -5 + 5 = 0
0 + y = 5.656854249 + 5
y = 5.656854249 + 5

Combine like terms: 5.656854249 + 5 = 10.656854249
y = 10.656854249

Simplifying
y = 10.656854249


Subproblem 2
y + -5 = -5.656854249

Simplifying
y + -5 = -5.656854249

Reorder the terms:
-5 + y = -5.656854249

Solving
-5 + y = -5.656854249

Solving for variable 'y'.

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

Add '5' to each side of the equation.
-5 + 5 + y = -5.656854249 + 5

Combine like terms: -5 + 5 = 0
0 + y = -5.656854249 + 5
y = -5.656854249 + 5

Combine like terms: -5.656854249 + 5 = -0.656854249
y = -0.656854249

Simplifying
y = -0.656854249


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {10.656854249, -0.656854249}

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