y^2=24-6y

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Solution for y^2=24-6y equation:


Simplifying
y2 = 24 + -6y

Solving
y2 = 24 + -6y

Solving for variable 'y'.

Reorder the terms:
-24 + 6y + y2 = 24 + -6y + -24 + 6y

Reorder the terms:
-24 + 6y + y2 = 24 + -24 + -6y + 6y

Combine like terms: 24 + -24 = 0
-24 + 6y + y2 = 0 + -6y + 6y
-24 + 6y + y2 = -6y + 6y

Combine like terms: -6y + 6y = 0
-24 + 6y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '24' to each side of the equation.
-24 + 6y + 24 + y2 = 0 + 24

Reorder the terms:
-24 + 24 + 6y + y2 = 0 + 24

Combine like terms: -24 + 24 = 0
0 + 6y + y2 = 0 + 24
6y + y2 = 0 + 24

Combine like terms: 0 + 24 = 24
6y + y2 = 24

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 = 24 + 9

Reorder the terms:
9 + 6y + y2 = 24 + 9

Combine like terms: 24 + 9 = 33
9 + 6y + y2 = 33

Factor a perfect square on the left side:
(y + 3)(y + 3) = 33

Calculate the square root of the right side: 5.744562647

Break this problem into two subproblems by setting 
(y + 3) equal to 5.744562647 and -5.744562647.

Subproblem 1

y + 3 = 5.744562647 Simplifying y + 3 = 5.744562647 Reorder the terms: 3 + y = 5.744562647 Solving 3 + y = 5.744562647 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 = 5.744562647 + -3 Combine like terms: 3 + -3 = 0 0 + y = 5.744562647 + -3 y = 5.744562647 + -3 Combine like terms: 5.744562647 + -3 = 2.744562647 y = 2.744562647 Simplifying y = 2.744562647

Subproblem 2

y + 3 = -5.744562647 Simplifying y + 3 = -5.744562647 Reorder the terms: 3 + y = -5.744562647 Solving 3 + y = -5.744562647 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 = -5.744562647 + -3 Combine like terms: 3 + -3 = 0 0 + y = -5.744562647 + -3 y = -5.744562647 + -3 Combine like terms: -5.744562647 + -3 = -8.744562647 y = -8.744562647 Simplifying y = -8.744562647

Solution

The solution to the problem is based on the solutions from the subproblems. y = {2.744562647, -8.744562647}

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