4y^8+36y^7+8y^6=

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Solution for 4y^8+36y^7+8y^6= equation:


Simplifying
4y8 + 36y7 + 8y6 = 0

Reorder the terms:
8y6 + 36y7 + 4y8 = 0

Solving
8y6 + 36y7 + 4y8 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '4y6'.
4y6(2 + 9y + y2) = 0

Ignore the factor 4.

Subproblem 1

Set the factor 'y6' equal to zero and attempt to solve: Simplifying y6 = 0 Solving y6 = 0 Move all terms containing y to the left, all other terms to the right. Simplifying y6 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 2

Set the factor '(2 + 9y + y2)' equal to zero and attempt to solve: Simplifying 2 + 9y + y2 = 0 Solving 2 + 9y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + 9y + -2 + y2 = 0 + -2 Reorder the terms: 2 + -2 + 9y + y2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 9y + y2 = 0 + -2 9y + y2 = 0 + -2 Combine like terms: 0 + -2 = -2 9y + y2 = -2 The y term is 9y. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9y + 20.25 + y2 = -2 + 20.25 Reorder the terms: 20.25 + 9y + y2 = -2 + 20.25 Combine like terms: -2 + 20.25 = 18.25 20.25 + 9y + y2 = 18.25 Factor a perfect square on the left side: (y + 4.5)(y + 4.5) = 18.25 Calculate the square root of the right side: 4.272001873 Break this problem into two subproblems by setting (y + 4.5) equal to 4.272001873 and -4.272001873.

Subproblem 1

y + 4.5 = 4.272001873 Simplifying y + 4.5 = 4.272001873 Reorder the terms: 4.5 + y = 4.272001873 Solving 4.5 + y = 4.272001873 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + y = 4.272001873 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + y = 4.272001873 + -4.5 y = 4.272001873 + -4.5 Combine like terms: 4.272001873 + -4.5 = -0.227998127 y = -0.227998127 Simplifying y = -0.227998127

Subproblem 2

y + 4.5 = -4.272001873 Simplifying y + 4.5 = -4.272001873 Reorder the terms: 4.5 + y = -4.272001873 Solving 4.5 + y = -4.272001873 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + y = -4.272001873 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + y = -4.272001873 + -4.5 y = -4.272001873 + -4.5 Combine like terms: -4.272001873 + -4.5 = -8.772001873 y = -8.772001873 Simplifying y = -8.772001873

Solution

The solution to the problem is based on the solutions from the subproblems. y = {-0.227998127, -8.772001873}

Solution

y = {-0.227998127, -8.772001873}

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