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Simplifying 3y3 + -15y2 + -2y = 0 Reorder the terms: -2y + -15y2 + 3y3 = 0 Solving -2y + -15y2 + 3y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), 'y'. y(-2 + -15y + 3y2) = 0Subproblem 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 + -15y + 3y2)' equal to zero and attempt to solve: Simplifying -2 + -15y + 3y2 = 0 Solving -2 + -15y + 3y2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -0.6666666667 + -5y + y2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + -5y + 0.6666666667 + y2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + -5y + y2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + -5y + y2 = 0 + 0.6666666667 -5y + y2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 -5y + y2 = 0.6666666667 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 = 0.6666666667 + 6.25 Reorder the terms: 6.25 + -5y + y2 = 0.6666666667 + 6.25 Combine like terms: 0.6666666667 + 6.25 = 6.9166666667 6.25 + -5y + y2 = 6.9166666667 Factor a perfect square on the left side: (y + -2.5)(y + -2.5) = 6.9166666667 Calculate the square root of the right side: 2.62995564 Break this problem into two subproblems by setting (y + -2.5) equal to 2.62995564 and -2.62995564.Subproblem 1
y + -2.5 = 2.62995564 Simplifying y + -2.5 = 2.62995564 Reorder the terms: -2.5 + y = 2.62995564 Solving -2.5 + y = 2.62995564 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 = 2.62995564 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + y = 2.62995564 + 2.5 y = 2.62995564 + 2.5 Combine like terms: 2.62995564 + 2.5 = 5.12995564 y = 5.12995564 Simplifying y = 5.12995564Subproblem 2
y + -2.5 = -2.62995564 Simplifying y + -2.5 = -2.62995564 Reorder the terms: -2.5 + y = -2.62995564 Solving -2.5 + y = -2.62995564 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 = -2.62995564 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + y = -2.62995564 + 2.5 y = -2.62995564 + 2.5 Combine like terms: -2.62995564 + 2.5 = -0.12995564 y = -0.12995564 Simplifying y = -0.12995564Solution
The solution to the problem is based on the solutions from the subproblems. y = {5.12995564, -0.12995564}Solution
y = {0, 5.12995564, -0.12995564}
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