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Simplifying 12y3 + -25y2 + 9y = 0 Reorder the terms: 9y + -25y2 + 12y3 = 0 Solving 9y + -25y2 + 12y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), 'y'. y(9 + -25y + 12y2) = 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 '(9 + -25y + 12y2)' equal to zero and attempt to solve: Simplifying 9 + -25y + 12y2 = 0 Solving 9 + -25y + 12y2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 0.75 + -2.083333333y + y2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + -2.083333333y + -0.75 + y2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + -2.083333333y + y2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + -2.083333333y + y2 = 0 + -0.75 -2.083333333y + y2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 -2.083333333y + y2 = -0.75 The y term is -2.083333333y. Take half its coefficient (-1.041666667). Square it (1.085069445) and add it to both sides. Add '1.085069445' to each side of the equation. -2.083333333y + 1.085069445 + y2 = -0.75 + 1.085069445 Reorder the terms: 1.085069445 + -2.083333333y + y2 = -0.75 + 1.085069445 Combine like terms: -0.75 + 1.085069445 = 0.335069445 1.085069445 + -2.083333333y + y2 = 0.335069445 Factor a perfect square on the left side: (y + -1.041666667)(y + -1.041666667) = 0.335069445 Calculate the square root of the right side: 0.578851833 Break this problem into two subproblems by setting (y + -1.041666667) equal to 0.578851833 and -0.578851833.Subproblem 1
y + -1.041666667 = 0.578851833 Simplifying y + -1.041666667 = 0.578851833 Reorder the terms: -1.041666667 + y = 0.578851833 Solving -1.041666667 + y = 0.578851833 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.041666667' to each side of the equation. -1.041666667 + 1.041666667 + y = 0.578851833 + 1.041666667 Combine like terms: -1.041666667 + 1.041666667 = 0.000000000 0.000000000 + y = 0.578851833 + 1.041666667 y = 0.578851833 + 1.041666667 Combine like terms: 0.578851833 + 1.041666667 = 1.6205185 y = 1.6205185 Simplifying y = 1.6205185Subproblem 2
y + -1.041666667 = -0.578851833 Simplifying y + -1.041666667 = -0.578851833 Reorder the terms: -1.041666667 + y = -0.578851833 Solving -1.041666667 + y = -0.578851833 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.041666667' to each side of the equation. -1.041666667 + 1.041666667 + y = -0.578851833 + 1.041666667 Combine like terms: -1.041666667 + 1.041666667 = 0.000000000 0.000000000 + y = -0.578851833 + 1.041666667 y = -0.578851833 + 1.041666667 Combine like terms: -0.578851833 + 1.041666667 = 0.462814834 y = 0.462814834 Simplifying y = 0.462814834Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.6205185, 0.462814834}Solution
y = {0, 1.6205185, 0.462814834}
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