y^2+6y-28=0

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Solution for y^2+6y-28=0 equation: 


Simplifying
y2 + 6y + -28 = 0

Reorder the terms:
-28 + 6y + y2 = 0

Solving
-28 + 6y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '28' to each side of the equation.
-28 + 6y + 28 + y2 = 0 + 28

Reorder the terms:
-28 + 28 + 6y + y2 = 0 + 28

Combine like terms: -28 + 28 = 0
0 + 6y + y2 = 0 + 28
6y + y2 = 0 + 28

Combine like terms: 0 + 28 = 28
6y + y2 = 28

The y term is 6y.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6y + 9 + y2 = 28 + 9

Reorder the terms:
9 + 6y + y2 = 28 + 9

Combine like terms: 28 + 9 = 37
9 + 6y + y2 = 37

Factor a perfect square on the left side:
(y + 3)(y + 3) = 37

Calculate the square root of the right side: 6.08276253

Break this problem into two subproblems by setting 
(y + 3) equal to 6.08276253 and -6.08276253.


Subproblem 1
y + 3 = 6.08276253

Simplifying
y + 3 = 6.08276253

Reorder the terms:
3 + y = 6.08276253

Solving
3 + y = 6.08276253

Solving for variable 'y'.

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

Add '-3' to each side of the equation.
3 + -3 + y = 6.08276253 + -3

Combine like terms: 3 + -3 = 0
0 + y = 6.08276253 + -3
y = 6.08276253 + -3

Combine like terms: 6.08276253 + -3 = 3.08276253
y = 3.08276253

Simplifying
y = 3.08276253


Subproblem 2
y + 3 = -6.08276253

Simplifying
y + 3 = -6.08276253

Reorder the terms:
3 + y = -6.08276253

Solving
3 + y = -6.08276253

Solving for variable 'y'.

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

Add '-3' to each side of the equation.
3 + -3 + y = -6.08276253 + -3

Combine like terms: 3 + -3 = 0
0 + y = -6.08276253 + -3
y = -6.08276253 + -3

Combine like terms: -6.08276253 + -3 = -9.08276253
y = -9.08276253

Simplifying
y = -9.08276253


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {3.08276253, -9.08276253}

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