2y^2-35-7y=y^2-2

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Solution for 2y^2-35-7y=y^2-2 equation: 


Simplifying
2y2 + -35 + -7y = y2 + -2

Reorder the terms:
-35 + -7y + 2y2 = y2 + -2

Reorder the terms:
-35 + -7y + 2y2 = -2 + y2

Solving
-35 + -7y + 2y2 = -2 + y2

Solving for variable 'y'.

Reorder the terms:
-35 + 2 + -7y + 2y2 + -1y2 = -2 + y2 + 2 + -1y2

Combine like terms: -35 + 2 = -33
-33 + -7y + 2y2 + -1y2 = -2 + y2 + 2 + -1y2

Combine like terms: 2y2 + -1y2 = 1y2
-33 + -7y + 1y2 = -2 + y2 + 2 + -1y2

Reorder the terms:
-33 + -7y + 1y2 = -2 + 2 + y2 + -1y2

Combine like terms: -2 + 2 = 0
-33 + -7y + 1y2 = 0 + y2 + -1y2
-33 + -7y + 1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
-33 + -7y + 1y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '33' to each side of the equation.
-33 + -7y + 33 + y2 = 0 + 33

Reorder the terms:
-33 + 33 + -7y + y2 = 0 + 33

Combine like terms: -33 + 33 = 0
0 + -7y + y2 = 0 + 33
-7y + y2 = 0 + 33

Combine like terms: 0 + 33 = 33
-7y + y2 = 33

The y term is -7y.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7y + 12.25 + y2 = 33 + 12.25

Reorder the terms:
12.25 + -7y + y2 = 33 + 12.25

Combine like terms: 33 + 12.25 = 45.25
12.25 + -7y + y2 = 45.25

Factor a perfect square on the left side:
(y + -3.5)(y + -3.5) = 45.25

Calculate the square root of the right side: 6.726812024

Break this problem into two subproblems by setting 
(y + -3.5) equal to 6.726812024 and -6.726812024.


Subproblem 1
y + -3.5 = 6.726812024

Simplifying
y + -3.5 = 6.726812024

Reorder the terms:
-3.5 + y = 6.726812024

Solving
-3.5 + y = 6.726812024

Solving for variable 'y'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + y = 6.726812024 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + y = 6.726812024 + 3.5
y = 6.726812024 + 3.5

Combine like terms: 6.726812024 + 3.5 = 10.226812024
y = 10.226812024

Simplifying
y = 10.226812024


Subproblem 2
y + -3.5 = -6.726812024

Simplifying
y + -3.5 = -6.726812024

Reorder the terms:
-3.5 + y = -6.726812024

Solving
-3.5 + y = -6.726812024

Solving for variable 'y'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + y = -6.726812024 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + y = -6.726812024 + 3.5
y = -6.726812024 + 3.5

Combine like terms: -6.726812024 + 3.5 = -3.226812024
y = -3.226812024

Simplifying
y = -3.226812024


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {10.226812024, -3.226812024}

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