y^2+42.25=-13y

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Solution for y^2+42.25=-13y equation: 


Simplifying
y2 + 42.25 = -13y

Reorder the terms:
42.25 + y2 = -13y

Solving
42.25 + y2 = -13y

Solving for variable 'y'.

Reorder the terms:
42.25 + 13y + y2 = -13y + 13y

Combine like terms: -13y + 13y = 0
42.25 + 13y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-42.25' to each side of the equation.
42.25 + 13y + -42.25 + y2 = 0 + -42.25

Reorder the terms:
42.25 + -42.25 + 13y + y2 = 0 + -42.25

Combine like terms: 42.25 + -42.25 = 0.00
0.00 + 13y + y2 = 0 + -42.25
13y + y2 = 0 + -42.25

Combine like terms: 0 + -42.25 = -42.25
13y + y2 = -42.25

The y term is 13y.  Take half its coefficient (6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
13y + 42.25 + y2 = -42.25 + 42.25

Reorder the terms:
42.25 + 13y + y2 = -42.25 + 42.25

Combine like terms: -42.25 + 42.25 = 0.00
42.25 + 13y + y2 = 0.00

Factor a perfect square on the left side:
(y + 6.5)(y + 6.5) = 0.00

Calculate the square root of the right side: 0.00

Break this problem into two subproblems by setting 
(y + 6.5) equal to 0.00 and 0.00.


Subproblem 1
y + 6.5 = 0.00

Simplifying
y + 6.5 = 0.00

Reorder the terms:
6.5 + y = 0.00

Solving
6.5 + y = 0.00

Solving for variable 'y'.

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

Add '-6.5' to each side of the equation.
6.5 + -6.5 + y = 0.00 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + y = 0.00 + -6.5
y = 0.00 + -6.5

Combine like terms: 0.00 + -6.5 = -6.5
y = -6.5

Simplifying
y = -6.5


Subproblem 2
y + 6.5 = 0.00

Simplifying
y + 6.5 = 0.00

Reorder the terms:
6.5 + y = 0.00

Solving
6.5 + y = 0.00

Solving for variable 'y'.

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

Add '-6.5' to each side of the equation.
6.5 + -6.5 + y = 0.00 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + y = 0.00 + -6.5
y = 0.00 + -6.5

Combine like terms: 0.00 + -6.5 = -6.5
y = -6.5

Simplifying
y = -6.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-6.5, -6.5}

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