0=6-8y-y^2

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Solution for 0=6-8y-y^2 equation:


Simplifying
0 = 6 + -8y + -1y2

Solving
0 = 6 + -8y + -1y2

Solving for variable 'y'.

Combine like terms: 0 + -6 = -6
-6 + 8y + y2 = 6 + -8y + -1y2 + -6 + 8y + y2

Reorder the terms:
-6 + 8y + y2 = 6 + -6 + -8y + 8y + -1y2 + y2

Combine like terms: 6 + -6 = 0
-6 + 8y + y2 = 0 + -8y + 8y + -1y2 + y2
-6 + 8y + y2 = -8y + 8y + -1y2 + y2

Combine like terms: -8y + 8y = 0
-6 + 8y + y2 = 0 + -1y2 + y2
-6 + 8y + y2 = -1y2 + y2

Combine like terms: -1y2 + y2 = 0
-6 + 8y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 8y + 6 + y2 = 0 + 6

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

Combine like terms: -6 + 6 = 0
0 + 8y + y2 = 0 + 6
8y + y2 = 0 + 6

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

The y term is 8y.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8y + 16 + y2 = 6 + 16

Reorder the terms:
16 + 8y + y2 = 6 + 16

Combine like terms: 6 + 16 = 22
16 + 8y + y2 = 22

Factor a perfect square on the left side:
(y + 4)(y + 4) = 22

Calculate the square root of the right side: 4.69041576

Break this problem into two subproblems by setting 
(y + 4) equal to 4.69041576 and -4.69041576.

Subproblem 1

y + 4 = 4.69041576 Simplifying y + 4 = 4.69041576 Reorder the terms: 4 + y = 4.69041576 Solving 4 + y = 4.69041576 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + y = 4.69041576 + -4 Combine like terms: 4 + -4 = 0 0 + y = 4.69041576 + -4 y = 4.69041576 + -4 Combine like terms: 4.69041576 + -4 = 0.69041576 y = 0.69041576 Simplifying y = 0.69041576

Subproblem 2

y + 4 = -4.69041576 Simplifying y + 4 = -4.69041576 Reorder the terms: 4 + y = -4.69041576 Solving 4 + y = -4.69041576 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + y = -4.69041576 + -4 Combine like terms: 4 + -4 = 0 0 + y = -4.69041576 + -4 y = -4.69041576 + -4 Combine like terms: -4.69041576 + -4 = -8.69041576 y = -8.69041576 Simplifying y = -8.69041576

Solution

The solution to the problem is based on the solutions from the subproblems. y = {0.69041576, -8.69041576}

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