y^2-10y-3=0

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Solution for y^2-10y-3=0 equation: 


Simplifying
y2 + -10y + -3 = 0

Reorder the terms:
-3 + -10y + y2 = 0

Solving
-3 + -10y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -10y + 3 + y2 = 0 + 3

Reorder the terms:
-3 + 3 + -10y + y2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -10y + y2 = 0 + 3
-10y + y2 = 0 + 3

Combine like terms: 0 + 3 = 3
-10y + y2 = 3

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 = 3 + 25

Reorder the terms:
25 + -10y + y2 = 3 + 25

Combine like terms: 3 + 25 = 28
25 + -10y + y2 = 28

Factor a perfect square on the left side:
(y + -5)(y + -5) = 28

Calculate the square root of the right side: 5.291502622

Break this problem into two subproblems by setting 
(y + -5) equal to 5.291502622 and -5.291502622.


Subproblem 1
y + -5 = 5.291502622

Simplifying
y + -5 = 5.291502622

Reorder the terms:
-5 + y = 5.291502622

Solving
-5 + y = 5.291502622

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 = 5.291502622 + 5

Combine like terms: -5 + 5 = 0
0 + y = 5.291502622 + 5
y = 5.291502622 + 5

Combine like terms: 5.291502622 + 5 = 10.291502622
y = 10.291502622

Simplifying
y = 10.291502622


Subproblem 2
y + -5 = -5.291502622

Simplifying
y + -5 = -5.291502622

Reorder the terms:
-5 + y = -5.291502622

Solving
-5 + y = -5.291502622

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 = -5.291502622 + 5

Combine like terms: -5 + 5 = 0
0 + y = -5.291502622 + 5
y = -5.291502622 + 5

Combine like terms: -5.291502622 + 5 = -0.291502622
y = -0.291502622

Simplifying
y = -0.291502622


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {10.291502622, -0.291502622}

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