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Simplifying -1y3 + -10y2 + 27y = 0 Reorder the terms: 27y + -10y2 + -1y3 = 0 Solving 27y + -10y2 + -1y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), 'y'. y(27 + -10y + -1y2) = 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 '(27 + -10y + -1y2)' equal to zero and attempt to solve: Simplifying 27 + -10y + -1y2 = 0 Solving 27 + -10y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -27 + 10y + y2 = 0 Move the constant term to the right: Add '27' to each side of the equation. -27 + 10y + 27 + y2 = 0 + 27 Reorder the terms: -27 + 27 + 10y + y2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + 10y + y2 = 0 + 27 10y + y2 = 0 + 27 Combine like terms: 0 + 27 = 27 10y + y2 = 27 The y term is 10y. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10y + 25 + y2 = 27 + 25 Reorder the terms: 25 + 10y + y2 = 27 + 25 Combine like terms: 27 + 25 = 52 25 + 10y + y2 = 52 Factor a perfect square on the left side: (y + 5)(y + 5) = 52 Calculate the square root of the right side: 7.211102551 Break this problem into two subproblems by setting (y + 5) equal to 7.211102551 and -7.211102551.Subproblem 1
y + 5 = 7.211102551 Simplifying y + 5 = 7.211102551 Reorder the terms: 5 + y = 7.211102551 Solving 5 + y = 7.211102551 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + y = 7.211102551 + -5 Combine like terms: 5 + -5 = 0 0 + y = 7.211102551 + -5 y = 7.211102551 + -5 Combine like terms: 7.211102551 + -5 = 2.211102551 y = 2.211102551 Simplifying y = 2.211102551Subproblem 2
y + 5 = -7.211102551 Simplifying y + 5 = -7.211102551 Reorder the terms: 5 + y = -7.211102551 Solving 5 + y = -7.211102551 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + y = -7.211102551 + -5 Combine like terms: 5 + -5 = 0 0 + y = -7.211102551 + -5 y = -7.211102551 + -5 Combine like terms: -7.211102551 + -5 = -12.211102551 y = -12.211102551 Simplifying y = -12.211102551Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.211102551, -12.211102551}Solution
y = {0, 2.211102551, -12.211102551}
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