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Simplifying 2y3 + -11y2 + -12y = 0 Reorder the terms: -12y + -11y2 + 2y3 = 0 Solving -12y + -11y2 + 2y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), 'y'. y(-12 + -11y + 2y2) = 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 '(-12 + -11y + 2y2)' equal to zero and attempt to solve: Simplifying -12 + -11y + 2y2 = 0 Solving -12 + -11y + 2y2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -6 + -5.5y + y2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -5.5y + 6 + y2 = 0 + 6 Reorder the terms: -6 + 6 + -5.5y + y2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -5.5y + y2 = 0 + 6 -5.5y + y2 = 0 + 6 Combine like terms: 0 + 6 = 6 -5.5y + y2 = 6 The y term is -5.5y. Take half its coefficient (-2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. -5.5y + 7.5625 + y2 = 6 + 7.5625 Reorder the terms: 7.5625 + -5.5y + y2 = 6 + 7.5625 Combine like terms: 6 + 7.5625 = 13.5625 7.5625 + -5.5y + y2 = 13.5625 Factor a perfect square on the left side: (y + -2.75)(y + -2.75) = 13.5625 Calculate the square root of the right side: 3.682729966 Break this problem into two subproblems by setting (y + -2.75) equal to 3.682729966 and -3.682729966.Subproblem 1
y + -2.75 = 3.682729966 Simplifying y + -2.75 = 3.682729966 Reorder the terms: -2.75 + y = 3.682729966 Solving -2.75 + y = 3.682729966 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + y = 3.682729966 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + y = 3.682729966 + 2.75 y = 3.682729966 + 2.75 Combine like terms: 3.682729966 + 2.75 = 6.432729966 y = 6.432729966 Simplifying y = 6.432729966Subproblem 2
y + -2.75 = -3.682729966 Simplifying y + -2.75 = -3.682729966 Reorder the terms: -2.75 + y = -3.682729966 Solving -2.75 + y = -3.682729966 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + y = -3.682729966 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + y = -3.682729966 + 2.75 y = -3.682729966 + 2.75 Combine like terms: -3.682729966 + 2.75 = -0.932729966 y = -0.932729966 Simplifying y = -0.932729966Solution
The solution to the problem is based on the solutions from the subproblems. y = {6.432729966, -0.932729966}Solution
y = {0, 6.432729966, -0.932729966}
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