y^2+15y-7=0

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Solution for y^2+15y-7=0 equation: 


Simplifying
y2 + 15y + -7 = 0

Reorder the terms:
-7 + 15y + y2 = 0

Solving
-7 + 15y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + 15y + 7 + y2 = 0 + 7

Reorder the terms:
-7 + 7 + 15y + y2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 15y + y2 = 0 + 7
15y + y2 = 0 + 7

Combine like terms: 0 + 7 = 7
15y + y2 = 7

The y term is 15y.  Take half its coefficient (7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
15y + 56.25 + y2 = 7 + 56.25

Reorder the terms:
56.25 + 15y + y2 = 7 + 56.25

Combine like terms: 7 + 56.25 = 63.25
56.25 + 15y + y2 = 63.25

Factor a perfect square on the left side:
(y + 7.5)(y + 7.5) = 63.25

Calculate the square root of the right side: 7.95298686

Break this problem into two subproblems by setting 
(y + 7.5) equal to 7.95298686 and -7.95298686.


Subproblem 1
y + 7.5 = 7.95298686

Simplifying
y + 7.5 = 7.95298686

Reorder the terms:
7.5 + y = 7.95298686

Solving
7.5 + y = 7.95298686

Solving for variable 'y'.

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

Add '-7.5' to each side of the equation.
7.5 + -7.5 + y = 7.95298686 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + y = 7.95298686 + -7.5
y = 7.95298686 + -7.5

Combine like terms: 7.95298686 + -7.5 = 0.45298686
y = 0.45298686

Simplifying
y = 0.45298686


Subproblem 2
y + 7.5 = -7.95298686

Simplifying
y + 7.5 = -7.95298686

Reorder the terms:
7.5 + y = -7.95298686

Solving
7.5 + y = -7.95298686

Solving for variable 'y'.

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

Add '-7.5' to each side of the equation.
7.5 + -7.5 + y = -7.95298686 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + y = -7.95298686 + -7.5
y = -7.95298686 + -7.5

Combine like terms: -7.95298686 + -7.5 = -15.45298686
y = -15.45298686

Simplifying
y = -15.45298686


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.45298686, -15.45298686}

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