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Simplifying 3y3 + -10y2 + -3y = 0 Reorder the terms: -3y + -10y2 + 3y3 = 0 Solving -3y + -10y2 + 3y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), 'y'. y(-3 + -10y + 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 '(-3 + -10y + 3y2)' equal to zero and attempt to solve: Simplifying -3 + -10y + 3y2 = 0 Solving -3 + -10y + 3y2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1 + -3.333333333y + y2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -3.333333333y + 1 + y2 = 0 + 1 Reorder the terms: -1 + 1 + -3.333333333y + y2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -3.333333333y + y2 = 0 + 1 -3.333333333y + y2 = 0 + 1 Combine like terms: 0 + 1 = 1 -3.333333333y + y2 = 1 The y term is -3.333333333y. Take half its coefficient (-1.666666667). Square it (2.777777779) and add it to both sides. Add '2.777777779' to each side of the equation. -3.333333333y + 2.777777779 + y2 = 1 + 2.777777779 Reorder the terms: 2.777777779 + -3.333333333y + y2 = 1 + 2.777777779 Combine like terms: 1 + 2.777777779 = 3.777777779 2.777777779 + -3.333333333y + y2 = 3.777777779 Factor a perfect square on the left side: (y + -1.666666667)(y + -1.666666667) = 3.777777779 Calculate the square root of the right side: 1.943650632 Break this problem into two subproblems by setting (y + -1.666666667) equal to 1.943650632 and -1.943650632.Subproblem 1
y + -1.666666667 = 1.943650632 Simplifying y + -1.666666667 = 1.943650632 Reorder the terms: -1.666666667 + y = 1.943650632 Solving -1.666666667 + y = 1.943650632 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + y = 1.943650632 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + y = 1.943650632 + 1.666666667 y = 1.943650632 + 1.666666667 Combine like terms: 1.943650632 + 1.666666667 = 3.610317299 y = 3.610317299 Simplifying y = 3.610317299Subproblem 2
y + -1.666666667 = -1.943650632 Simplifying y + -1.666666667 = -1.943650632 Reorder the terms: -1.666666667 + y = -1.943650632 Solving -1.666666667 + y = -1.943650632 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + y = -1.943650632 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + y = -1.943650632 + 1.666666667 y = -1.943650632 + 1.666666667 Combine like terms: -1.943650632 + 1.666666667 = -0.276983965 y = -0.276983965 Simplifying y = -0.276983965Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.610317299, -0.276983965}Solution
y = {0, 3.610317299, -0.276983965}
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