y^2+14y-24=0

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Solution for y^2+14y-24=0 equation: 


Simplifying
y2 + 14y + -24 = 0

Reorder the terms:
-24 + 14y + y2 = 0

Solving
-24 + 14y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '24' to each side of the equation.
-24 + 14y + 24 + y2 = 0 + 24

Reorder the terms:
-24 + 24 + 14y + y2 = 0 + 24

Combine like terms: -24 + 24 = 0
0 + 14y + y2 = 0 + 24
14y + y2 = 0 + 24

Combine like terms: 0 + 24 = 24
14y + y2 = 24

The y term is 14y.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14y + 49 + y2 = 24 + 49

Reorder the terms:
49 + 14y + y2 = 24 + 49

Combine like terms: 24 + 49 = 73
49 + 14y + y2 = 73

Factor a perfect square on the left side:
(y + 7)(y + 7) = 73

Calculate the square root of the right side: 8.544003745

Break this problem into two subproblems by setting 
(y + 7) equal to 8.544003745 and -8.544003745.


Subproblem 1
y + 7 = 8.544003745

Simplifying
y + 7 = 8.544003745

Reorder the terms:
7 + y = 8.544003745

Solving
7 + y = 8.544003745

Solving for variable 'y'.

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

Add '-7' to each side of the equation.
7 + -7 + y = 8.544003745 + -7

Combine like terms: 7 + -7 = 0
0 + y = 8.544003745 + -7
y = 8.544003745 + -7

Combine like terms: 8.544003745 + -7 = 1.544003745
y = 1.544003745

Simplifying
y = 1.544003745


Subproblem 2
y + 7 = -8.544003745

Simplifying
y + 7 = -8.544003745

Reorder the terms:
7 + y = -8.544003745

Solving
7 + y = -8.544003745

Solving for variable 'y'.

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

Add '-7' to each side of the equation.
7 + -7 + y = -8.544003745 + -7

Combine like terms: 7 + -7 = 0
0 + y = -8.544003745 + -7
y = -8.544003745 + -7

Combine like terms: -8.544003745 + -7 = -15.544003745
y = -15.544003745

Simplifying
y = -15.544003745


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.544003745, -15.544003745}

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