y^2+24y+92=0

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Solution for y^2+24y+92=0 equation: 


Simplifying
y2 + 24y + 92 = 0

Reorder the terms:
92 + 24y + y2 = 0

Solving
92 + 24y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-92' to each side of the equation.
92 + 24y + -92 + y2 = 0 + -92

Reorder the terms:
92 + -92 + 24y + y2 = 0 + -92

Combine like terms: 92 + -92 = 0
0 + 24y + y2 = 0 + -92
24y + y2 = 0 + -92

Combine like terms: 0 + -92 = -92
24y + y2 = -92

The y term is 24y.  Take half its coefficient (12).
Square it (144) and add it to both sides.

Add '144' to each side of the equation.
24y + 144 + y2 = -92 + 144

Reorder the terms:
144 + 24y + y2 = -92 + 144

Combine like terms: -92 + 144 = 52
144 + 24y + y2 = 52

Factor a perfect square on the left side:
(y + 12)(y + 12) = 52

Calculate the square root of the right side: 7.211102551

Break this problem into two subproblems by setting 
(y + 12) equal to 7.211102551 and -7.211102551.


Subproblem 1
y + 12 = 7.211102551

Simplifying
y + 12 = 7.211102551

Reorder the terms:
12 + y = 7.211102551

Solving
12 + y = 7.211102551

Solving for variable 'y'.

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

Add '-12' to each side of the equation.
12 + -12 + y = 7.211102551 + -12

Combine like terms: 12 + -12 = 0
0 + y = 7.211102551 + -12
y = 7.211102551 + -12

Combine like terms: 7.211102551 + -12 = -4.788897449
y = -4.788897449

Simplifying
y = -4.788897449


Subproblem 2
y + 12 = -7.211102551

Simplifying
y + 12 = -7.211102551

Reorder the terms:
12 + y = -7.211102551

Solving
12 + y = -7.211102551

Solving for variable 'y'.

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

Add '-12' to each side of the equation.
12 + -12 + y = -7.211102551 + -12

Combine like terms: 12 + -12 = 0
0 + y = -7.211102551 + -12
y = -7.211102551 + -12

Combine like terms: -7.211102551 + -12 = -19.211102551
y = -19.211102551

Simplifying
y = -19.211102551


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-4.788897449, -19.211102551}

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