y^2+30y+7=0

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Solution for y^2+30y+7=0 equation: 


Simplifying
y2 + 30y + 7 = 0

Reorder the terms:
7 + 30y + y2 = 0

Solving
7 + 30y + 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 + 30y + -7 + y2 = 0 + -7

Reorder the terms:
7 + -7 + 30y + y2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 30y + y2 = 0 + -7
30y + y2 = 0 + -7

Combine like terms: 0 + -7 = -7
30y + y2 = -7

The y term is 30y.  Take half its coefficient (15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
30y + 225 + y2 = -7 + 225

Reorder the terms:
225 + 30y + y2 = -7 + 225

Combine like terms: -7 + 225 = 218
225 + 30y + y2 = 218

Factor a perfect square on the left side:
(y + 15)(y + 15) = 218

Calculate the square root of the right side: 14.76482306

Break this problem into two subproblems by setting 
(y + 15) equal to 14.76482306 and -14.76482306.


Subproblem 1
y + 15 = 14.76482306

Simplifying
y + 15 = 14.76482306

Reorder the terms:
15 + y = 14.76482306

Solving
15 + y = 14.76482306

Solving for variable 'y'.

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

Add '-15' to each side of the equation.
15 + -15 + y = 14.76482306 + -15

Combine like terms: 15 + -15 = 0
0 + y = 14.76482306 + -15
y = 14.76482306 + -15

Combine like terms: 14.76482306 + -15 = -0.23517694
y = -0.23517694

Simplifying
y = -0.23517694


Subproblem 2
y + 15 = -14.76482306

Simplifying
y + 15 = -14.76482306

Reorder the terms:
15 + y = -14.76482306

Solving
15 + y = -14.76482306

Solving for variable 'y'.

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

Add '-15' to each side of the equation.
15 + -15 + y = -14.76482306 + -15

Combine like terms: 15 + -15 = 0
0 + y = -14.76482306 + -15
y = -14.76482306 + -15

Combine like terms: -14.76482306 + -15 = -29.76482306
y = -29.76482306

Simplifying
y = -29.76482306


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-0.23517694, -29.76482306}

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