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Simplifying 5y3 + -50y2 + 12y = 0 Reorder the terms: 12y + -50y2 + 5y3 = 0 Solving 12y + -50y2 + 5y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), 'y'. y(12 + -50y + 5y2) = 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 + -50y + 5y2)' equal to zero and attempt to solve: Simplifying 12 + -50y + 5y2 = 0 Solving 12 + -50y + 5y2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 2.4 + -10y + y2 = 0 Move the constant term to the right: Add '-2.4' to each side of the equation. 2.4 + -10y + -2.4 + y2 = 0 + -2.4 Reorder the terms: 2.4 + -2.4 + -10y + y2 = 0 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + -10y + y2 = 0 + -2.4 -10y + y2 = 0 + -2.4 Combine like terms: 0 + -2.4 = -2.4 -10y + y2 = -2.4 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 = -2.4 + 25 Reorder the terms: 25 + -10y + y2 = -2.4 + 25 Combine like terms: -2.4 + 25 = 22.6 25 + -10y + y2 = 22.6 Factor a perfect square on the left side: (y + -5)(y + -5) = 22.6 Calculate the square root of the right side: 4.75394573 Break this problem into two subproblems by setting (y + -5) equal to 4.75394573 and -4.75394573.Subproblem 1
y + -5 = 4.75394573 Simplifying y + -5 = 4.75394573 Reorder the terms: -5 + y = 4.75394573 Solving -5 + y = 4.75394573 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 = 4.75394573 + 5 Combine like terms: -5 + 5 = 0 0 + y = 4.75394573 + 5 y = 4.75394573 + 5 Combine like terms: 4.75394573 + 5 = 9.75394573 y = 9.75394573 Simplifying y = 9.75394573Subproblem 2
y + -5 = -4.75394573 Simplifying y + -5 = -4.75394573 Reorder the terms: -5 + y = -4.75394573 Solving -5 + y = -4.75394573 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 = -4.75394573 + 5 Combine like terms: -5 + 5 = 0 0 + y = -4.75394573 + 5 y = -4.75394573 + 5 Combine like terms: -4.75394573 + 5 = 0.24605427 y = 0.24605427 Simplifying y = 0.24605427Solution
The solution to the problem is based on the solutions from the subproblems. y = {9.75394573, 0.24605427}Solution
y = {0, 9.75394573, 0.24605427}
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