y^2+12y=y-5

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Solution for y^2+12y=y-5 equation:


Simplifying
y2 + 12y = y + -5

Reorder the terms:
12y + y2 = y + -5

Reorder the terms:
12y + y2 = -5 + y

Solving
12y + y2 = -5 + y

Solving for variable 'y'.

Reorder the terms:
5 + 12y + -1y + y2 = -5 + y + 5 + -1y

Combine like terms: 12y + -1y = 11y
5 + 11y + y2 = -5 + y + 5 + -1y

Reorder the terms:
5 + 11y + y2 = -5 + 5 + y + -1y

Combine like terms: -5 + 5 = 0
5 + 11y + y2 = 0 + y + -1y
5 + 11y + y2 = y + -1y

Combine like terms: y + -1y = 0
5 + 11y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + 11y + -5 + y2 = 0 + -5

Reorder the terms:
5 + -5 + 11y + y2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 11y + y2 = 0 + -5
11y + y2 = 0 + -5

Combine like terms: 0 + -5 = -5
11y + y2 = -5

The y term is 11y.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11y + 30.25 + y2 = -5 + 30.25

Reorder the terms:
30.25 + 11y + y2 = -5 + 30.25

Combine like terms: -5 + 30.25 = 25.25
30.25 + 11y + y2 = 25.25

Factor a perfect square on the left side:
(y + 5.5)(y + 5.5) = 25.25

Calculate the square root of the right side: 5.024937811

Break this problem into two subproblems by setting 
(y + 5.5) equal to 5.024937811 and -5.024937811.

Subproblem 1

y + 5.5 = 5.024937811 Simplifying y + 5.5 = 5.024937811 Reorder the terms: 5.5 + y = 5.024937811 Solving 5.5 + y = 5.024937811 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + y = 5.024937811 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + y = 5.024937811 + -5.5 y = 5.024937811 + -5.5 Combine like terms: 5.024937811 + -5.5 = -0.475062189 y = -0.475062189 Simplifying y = -0.475062189

Subproblem 2

y + 5.5 = -5.024937811 Simplifying y + 5.5 = -5.024937811 Reorder the terms: 5.5 + y = -5.024937811 Solving 5.5 + y = -5.024937811 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + y = -5.024937811 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + y = -5.024937811 + -5.5 y = -5.024937811 + -5.5 Combine like terms: -5.024937811 + -5.5 = -10.524937811 y = -10.524937811 Simplifying y = -10.524937811

Solution

The solution to the problem is based on the solutions from the subproblems. y = {-0.475062189, -10.524937811}

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