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Simplifying 3y3 + -20y2 + -3y = 0 Reorder the terms: -3y + -20y2 + 3y3 = 0 Solving -3y + -20y2 + 3y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), 'y'. y(-3 + -20y + 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 + -20y + 3y2)' equal to zero and attempt to solve: Simplifying -3 + -20y + 3y2 = 0 Solving -3 + -20y + 3y2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1 + -6.666666667y + y2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -6.666666667y + 1 + y2 = 0 + 1 Reorder the terms: -1 + 1 + -6.666666667y + y2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -6.666666667y + y2 = 0 + 1 -6.666666667y + y2 = 0 + 1 Combine like terms: 0 + 1 = 1 -6.666666667y + y2 = 1 The y term is -6.666666667y. Take half its coefficient (-3.333333334). Square it (11.11111112) and add it to both sides. Add '11.11111112' to each side of the equation. -6.666666667y + 11.11111112 + y2 = 1 + 11.11111112 Reorder the terms: 11.11111112 + -6.666666667y + y2 = 1 + 11.11111112 Combine like terms: 1 + 11.11111112 = 12.11111112 11.11111112 + -6.666666667y + y2 = 12.11111112 Factor a perfect square on the left side: (y + -3.333333334)(y + -3.333333334) = 12.11111112 Calculate the square root of the right side: 3.480102171 Break this problem into two subproblems by setting (y + -3.333333334) equal to 3.480102171 and -3.480102171.Subproblem 1
y + -3.333333334 = 3.480102171 Simplifying y + -3.333333334 = 3.480102171 Reorder the terms: -3.333333334 + y = 3.480102171 Solving -3.333333334 + y = 3.480102171 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.333333334' to each side of the equation. -3.333333334 + 3.333333334 + y = 3.480102171 + 3.333333334 Combine like terms: -3.333333334 + 3.333333334 = 0.000000000 0.000000000 + y = 3.480102171 + 3.333333334 y = 3.480102171 + 3.333333334 Combine like terms: 3.480102171 + 3.333333334 = 6.813435505 y = 6.813435505 Simplifying y = 6.813435505Subproblem 2
y + -3.333333334 = -3.480102171 Simplifying y + -3.333333334 = -3.480102171 Reorder the terms: -3.333333334 + y = -3.480102171 Solving -3.333333334 + y = -3.480102171 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.333333334' to each side of the equation. -3.333333334 + 3.333333334 + y = -3.480102171 + 3.333333334 Combine like terms: -3.333333334 + 3.333333334 = 0.000000000 0.000000000 + y = -3.480102171 + 3.333333334 y = -3.480102171 + 3.333333334 Combine like terms: -3.480102171 + 3.333333334 = -0.146768837 y = -0.146768837 Simplifying y = -0.146768837Solution
The solution to the problem is based on the solutions from the subproblems. y = {6.813435505, -0.146768837}Solution
y = {0, 6.813435505, -0.146768837}
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