y^2-3y-35=0

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Solution for y^2-3y-35=0 equation: 


Simplifying
y2 + -3y + -35 = 0

Reorder the terms:
-35 + -3y + y2 = 0

Solving
-35 + -3y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '35' to each side of the equation.
-35 + -3y + 35 + y2 = 0 + 35

Reorder the terms:
-35 + 35 + -3y + y2 = 0 + 35

Combine like terms: -35 + 35 = 0
0 + -3y + y2 = 0 + 35
-3y + y2 = 0 + 35

Combine like terms: 0 + 35 = 35
-3y + y2 = 35

The y term is -3y.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3y + 2.25 + y2 = 35 + 2.25

Reorder the terms:
2.25 + -3y + y2 = 35 + 2.25

Combine like terms: 35 + 2.25 = 37.25
2.25 + -3y + y2 = 37.25

Factor a perfect square on the left side:
(y + -1.5)(y + -1.5) = 37.25

Calculate the square root of the right side: 6.103277808

Break this problem into two subproblems by setting 
(y + -1.5) equal to 6.103277808 and -6.103277808.


Subproblem 1
y + -1.5 = 6.103277808

Simplifying
y + -1.5 = 6.103277808

Reorder the terms:
-1.5 + y = 6.103277808

Solving
-1.5 + y = 6.103277808

Solving for variable 'y'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + y = 6.103277808 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + y = 6.103277808 + 1.5
y = 6.103277808 + 1.5

Combine like terms: 6.103277808 + 1.5 = 7.603277808
y = 7.603277808

Simplifying
y = 7.603277808


Subproblem 2
y + -1.5 = -6.103277808

Simplifying
y + -1.5 = -6.103277808

Reorder the terms:
-1.5 + y = -6.103277808

Solving
-1.5 + y = -6.103277808

Solving for variable 'y'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + y = -6.103277808 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + y = -6.103277808 + 1.5
y = -6.103277808 + 1.5

Combine like terms: -6.103277808 + 1.5 = -4.603277808
y = -4.603277808

Simplifying
y = -4.603277808


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {7.603277808, -4.603277808}

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