y^2-35y-2=0

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Solution for y^2-35y-2=0 equation: 


Simplifying
y2 + -35y + -2 = 0

Reorder the terms:
-2 + -35y + y2 = 0

Solving
-2 + -35y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -35y + 2 + y2 = 0 + 2

Reorder the terms:
-2 + 2 + -35y + y2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -35y + y2 = 0 + 2
-35y + y2 = 0 + 2

Combine like terms: 0 + 2 = 2
-35y + y2 = 2

The y term is -35y.  Take half its coefficient (-17.5).
Square it (306.25) and add it to both sides.

Add '306.25' to each side of the equation.
-35y + 306.25 + y2 = 2 + 306.25

Reorder the terms:
306.25 + -35y + y2 = 2 + 306.25

Combine like terms: 2 + 306.25 = 308.25
306.25 + -35y + y2 = 308.25

Factor a perfect square on the left side:
(y + -17.5)(y + -17.5) = 308.25

Calculate the square root of the right side: 17.557049866

Break this problem into two subproblems by setting 
(y + -17.5) equal to 17.557049866 and -17.557049866.


Subproblem 1
y + -17.5 = 17.557049866

Simplifying
y + -17.5 = 17.557049866

Reorder the terms:
-17.5 + y = 17.557049866

Solving
-17.5 + y = 17.557049866

Solving for variable 'y'.

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

Add '17.5' to each side of the equation.
-17.5 + 17.5 + y = 17.557049866 + 17.5

Combine like terms: -17.5 + 17.5 = 0.0
0.0 + y = 17.557049866 + 17.5
y = 17.557049866 + 17.5

Combine like terms: 17.557049866 + 17.5 = 35.057049866
y = 35.057049866

Simplifying
y = 35.057049866


Subproblem 2
y + -17.5 = -17.557049866

Simplifying
y + -17.5 = -17.557049866

Reorder the terms:
-17.5 + y = -17.557049866

Solving
-17.5 + y = -17.557049866

Solving for variable 'y'.

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

Add '17.5' to each side of the equation.
-17.5 + 17.5 + y = -17.557049866 + 17.5

Combine like terms: -17.5 + 17.5 = 0.0
0.0 + y = -17.557049866 + 17.5
y = -17.557049866 + 17.5

Combine like terms: -17.557049866 + 17.5 = -0.057049866
y = -0.057049866

Simplifying
y = -0.057049866


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {35.057049866, -0.057049866}

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