y^2+6y+8y+25=0

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Solution for y^2+6y+8y+25=0 equation: 


Simplifying
y2 + 6y + 8y + 25 = 0

Reorder the terms:
25 + 6y + 8y + y2 = 0

Combine like terms: 6y + 8y = 14y
25 + 14y + y2 = 0

Solving
25 + 14y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-25' to each side of the equation.
25 + 14y + -25 + y2 = 0 + -25

Reorder the terms:
25 + -25 + 14y + y2 = 0 + -25

Combine like terms: 25 + -25 = 0
0 + 14y + y2 = 0 + -25
14y + y2 = 0 + -25

Combine like terms: 0 + -25 = -25
14y + y2 = -25

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 = -25 + 49

Reorder the terms:
49 + 14y + y2 = -25 + 49

Combine like terms: -25 + 49 = 24
49 + 14y + y2 = 24

Factor a perfect square on the left side:
(y + 7)(y + 7) = 24

Calculate the square root of the right side: 4.898979486

Break this problem into two subproblems by setting 
(y + 7) equal to 4.898979486 and -4.898979486.


Subproblem 1
y + 7 = 4.898979486

Simplifying
y + 7 = 4.898979486

Reorder the terms:
7 + y = 4.898979486

Solving
7 + y = 4.898979486

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 = 4.898979486 + -7

Combine like terms: 7 + -7 = 0
0 + y = 4.898979486 + -7
y = 4.898979486 + -7

Combine like terms: 4.898979486 + -7 = -2.101020514
y = -2.101020514

Simplifying
y = -2.101020514


Subproblem 2
y + 7 = -4.898979486

Simplifying
y + 7 = -4.898979486

Reorder the terms:
7 + y = -4.898979486

Solving
7 + y = -4.898979486

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 = -4.898979486 + -7

Combine like terms: 7 + -7 = 0
0 + y = -4.898979486 + -7
y = -4.898979486 + -7

Combine like terms: -4.898979486 + -7 = -11.898979486
y = -11.898979486

Simplifying
y = -11.898979486


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-2.101020514, -11.898979486}

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