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Simplifying 5y3 + 20y2 + -10y = 0 Reorder the terms: -10y + 20y2 + 5y3 = 0 Solving -10y + 20y2 + 5y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '5y'. 5y(-2 + 4y + y2) = 0 Ignore the factor 5.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 = 0Subproblem 2
Set the factor '(-2 + 4y + y2)' equal to zero and attempt to solve: Simplifying -2 + 4y + y2 = 0 Solving -2 + 4y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + 4y + 2 + y2 = 0 + 2 Reorder the terms: -2 + 2 + 4y + y2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 4y + y2 = 0 + 2 4y + y2 = 0 + 2 Combine like terms: 0 + 2 = 2 4y + y2 = 2 The y term is 4y. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4y + 4 + y2 = 2 + 4 Reorder the terms: 4 + 4y + y2 = 2 + 4 Combine like terms: 2 + 4 = 6 4 + 4y + y2 = 6 Factor a perfect square on the left side: (y + 2)(y + 2) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (y + 2) equal to 2.449489743 and -2.449489743.Subproblem 1
y + 2 = 2.449489743 Simplifying y + 2 = 2.449489743 Reorder the terms: 2 + y = 2.449489743 Solving 2 + y = 2.449489743 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + y = 2.449489743 + -2 Combine like terms: 2 + -2 = 0 0 + y = 2.449489743 + -2 y = 2.449489743 + -2 Combine like terms: 2.449489743 + -2 = 0.449489743 y = 0.449489743 Simplifying y = 0.449489743Subproblem 2
y + 2 = -2.449489743 Simplifying y + 2 = -2.449489743 Reorder the terms: 2 + y = -2.449489743 Solving 2 + y = -2.449489743 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + y = -2.449489743 + -2 Combine like terms: 2 + -2 = 0 0 + y = -2.449489743 + -2 y = -2.449489743 + -2 Combine like terms: -2.449489743 + -2 = -4.449489743 y = -4.449489743 Simplifying y = -4.449489743Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.449489743, -4.449489743}Solution
y = {0, 0.449489743, -4.449489743}
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