2y^3+2y=10y^2

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Solution for 2y^3+2y=10y^2 equation:


Simplifying
2y3 + 2y = 10y2

Reorder the terms:
2y + 2y3 = 10y2

Solving
2y + 2y3 = 10y2

Solving for variable 'y'.

Reorder the terms:
2y + -10y2 + 2y3 = 10y2 + -10y2

Combine like terms: 10y2 + -10y2 = 0
2y + -10y2 + 2y3 = 0

Factor out the Greatest Common Factor (GCF), '2y'.
2y(1 + -5y + y2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor 'y' equal to zero and attempt to solve: Simplifying y = 0 Solving y = 0 Move all terms containing y to the left, all other terms to the right. Simplifying y = 0

Subproblem 2

Set the factor '(1 + -5y + y2)' equal to zero and attempt to solve: Simplifying 1 + -5y + y2 = 0 Solving 1 + -5y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -5y + -1 + y2 = 0 + -1 Reorder the terms: 1 + -1 + -5y + y2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5y + y2 = 0 + -1 -5y + y2 = 0 + -1 Combine like terms: 0 + -1 = -1 -5y + y2 = -1 The y term is -5y. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5y + 6.25 + y2 = -1 + 6.25 Reorder the terms: 6.25 + -5y + y2 = -1 + 6.25 Combine like terms: -1 + 6.25 = 5.25 6.25 + -5y + y2 = 5.25 Factor a perfect square on the left side: (y + -2.5)(y + -2.5) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (y + -2.5) equal to 2.291287847 and -2.291287847.

Subproblem 1

y + -2.5 = 2.291287847 Simplifying y + -2.5 = 2.291287847 Reorder the terms: -2.5 + y = 2.291287847 Solving -2.5 + y = 2.291287847 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + y = 2.291287847 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + y = 2.291287847 + 2.5 y = 2.291287847 + 2.5 Combine like terms: 2.291287847 + 2.5 = 4.791287847 y = 4.791287847 Simplifying y = 4.791287847

Subproblem 2

y + -2.5 = -2.291287847 Simplifying y + -2.5 = -2.291287847 Reorder the terms: -2.5 + y = -2.291287847 Solving -2.5 + y = -2.291287847 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + y = -2.291287847 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + y = -2.291287847 + 2.5 y = -2.291287847 + 2.5 Combine like terms: -2.291287847 + 2.5 = 0.208712153 y = 0.208712153 Simplifying y = 0.208712153

Solution

The solution to the problem is based on the solutions from the subproblems. y = {4.791287847, 0.208712153}

Solution

y = {0, 4.791287847, 0.208712153}

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