y^2+6y-6=-3

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Solution for y^2+6y-6=-3 equation:


Simplifying
y2 + 6y + -6 = -3

Reorder the terms:
-6 + 6y + y2 = -3

Solving
-6 + 6y + y2 = -3

Solving for variable 'y'.

Reorder the terms:
-6 + 3 + 6y + y2 = -3 + 3

Combine like terms: -6 + 3 = -3
-3 + 6y + y2 = -3 + 3

Combine like terms: -3 + 3 = 0
-3 + 6y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 6y + 3 + y2 = 0 + 3

Reorder the terms:
-3 + 3 + 6y + y2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 6y + y2 = 0 + 3
6y + y2 = 0 + 3

Combine like terms: 0 + 3 = 3
6y + y2 = 3

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 = 3 + 9

Reorder the terms:
9 + 6y + y2 = 3 + 9

Combine like terms: 3 + 9 = 12
9 + 6y + y2 = 12

Factor a perfect square on the left side:
(y + 3)(y + 3) = 12

Calculate the square root of the right side: 3.464101615

Break this problem into two subproblems by setting 
(y + 3) equal to 3.464101615 and -3.464101615.

Subproblem 1

y + 3 = 3.464101615 Simplifying y + 3 = 3.464101615 Reorder the terms: 3 + y = 3.464101615 Solving 3 + y = 3.464101615 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 = 3.464101615 + -3 Combine like terms: 3 + -3 = 0 0 + y = 3.464101615 + -3 y = 3.464101615 + -3 Combine like terms: 3.464101615 + -3 = 0.464101615 y = 0.464101615 Simplifying y = 0.464101615

Subproblem 2

y + 3 = -3.464101615 Simplifying y + 3 = -3.464101615 Reorder the terms: 3 + y = -3.464101615 Solving 3 + y = -3.464101615 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 = -3.464101615 + -3 Combine like terms: 3 + -3 = 0 0 + y = -3.464101615 + -3 y = -3.464101615 + -3 Combine like terms: -3.464101615 + -3 = -6.464101615 y = -6.464101615 Simplifying y = -6.464101615

Solution

The solution to the problem is based on the solutions from the subproblems. y = {0.464101615, -6.464101615}

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