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Simplifying -3y3 + -6y2 + 2y = 0 Reorder the terms: 2y + -6y2 + -3y3 = 0 Solving 2y + -6y2 + -3y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), 'y'. y(2 + -6y + -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 + -6y + -3y2)' equal to zero and attempt to solve: Simplifying 2 + -6y + -3y2 = 0 Solving 2 + -6y + -3y2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -0.6666666667 + 2y + y2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + 2y + 0.6666666667 + y2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + 2y + y2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + 2y + y2 = 0 + 0.6666666667 2y + y2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 2y + y2 = 0.6666666667 The y term is 2y. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2y + 1 + y2 = 0.6666666667 + 1 Reorder the terms: 1 + 2y + y2 = 0.6666666667 + 1 Combine like terms: 0.6666666667 + 1 = 1.6666666667 1 + 2y + y2 = 1.6666666667 Factor a perfect square on the left side: (y + 1)(y + 1) = 1.6666666667 Calculate the square root of the right side: 1.290994449 Break this problem into two subproblems by setting (y + 1) equal to 1.290994449 and -1.290994449.Subproblem 1
y + 1 = 1.290994449 Simplifying y + 1 = 1.290994449 Reorder the terms: 1 + y = 1.290994449 Solving 1 + y = 1.290994449 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y = 1.290994449 + -1 Combine like terms: 1 + -1 = 0 0 + y = 1.290994449 + -1 y = 1.290994449 + -1 Combine like terms: 1.290994449 + -1 = 0.290994449 y = 0.290994449 Simplifying y = 0.290994449Subproblem 2
y + 1 = -1.290994449 Simplifying y + 1 = -1.290994449 Reorder the terms: 1 + y = -1.290994449 Solving 1 + y = -1.290994449 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y = -1.290994449 + -1 Combine like terms: 1 + -1 = 0 0 + y = -1.290994449 + -1 y = -1.290994449 + -1 Combine like terms: -1.290994449 + -1 = -2.290994449 y = -2.290994449 Simplifying y = -2.290994449Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.290994449, -2.290994449}Solution
y = {0, 0.290994449, -2.290994449}
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