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Simplifying 9y3 + -21y2 + -10y = 0 Reorder the terms: -10y + -21y2 + 9y3 = 0 Solving -10y + -21y2 + 9y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), 'y'. y(-10 + -21y + 9y2) = 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 '(-10 + -21y + 9y2)' equal to zero and attempt to solve: Simplifying -10 + -21y + 9y2 = 0 Solving -10 + -21y + 9y2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.111111111 + -2.333333333y + y2 = 0 Move the constant term to the right: Add '1.111111111' to each side of the equation. -1.111111111 + -2.333333333y + 1.111111111 + y2 = 0 + 1.111111111 Reorder the terms: -1.111111111 + 1.111111111 + -2.333333333y + y2 = 0 + 1.111111111 Combine like terms: -1.111111111 + 1.111111111 = 0.000000000 0.000000000 + -2.333333333y + y2 = 0 + 1.111111111 -2.333333333y + y2 = 0 + 1.111111111 Combine like terms: 0 + 1.111111111 = 1.111111111 -2.333333333y + y2 = 1.111111111 The y term is -2.333333333y. Take half its coefficient (-1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. -2.333333333y + 1.361111112 + y2 = 1.111111111 + 1.361111112 Reorder the terms: 1.361111112 + -2.333333333y + y2 = 1.111111111 + 1.361111112 Combine like terms: 1.111111111 + 1.361111112 = 2.472222223 1.361111112 + -2.333333333y + y2 = 2.472222223 Factor a perfect square on the left side: (y + -1.166666667)(y + -1.166666667) = 2.472222223 Calculate the square root of the right side: 1.572330189 Break this problem into two subproblems by setting (y + -1.166666667) equal to 1.572330189 and -1.572330189.Subproblem 1
y + -1.166666667 = 1.572330189 Simplifying y + -1.166666667 = 1.572330189 Reorder the terms: -1.166666667 + y = 1.572330189 Solving -1.166666667 + y = 1.572330189 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + y = 1.572330189 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + y = 1.572330189 + 1.166666667 y = 1.572330189 + 1.166666667 Combine like terms: 1.572330189 + 1.166666667 = 2.738996856 y = 2.738996856 Simplifying y = 2.738996856Subproblem 2
y + -1.166666667 = -1.572330189 Simplifying y + -1.166666667 = -1.572330189 Reorder the terms: -1.166666667 + y = -1.572330189 Solving -1.166666667 + y = -1.572330189 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + y = -1.572330189 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + y = -1.572330189 + 1.166666667 y = -1.572330189 + 1.166666667 Combine like terms: -1.572330189 + 1.166666667 = -0.405663522 y = -0.405663522 Simplifying y = -0.405663522Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.738996856, -0.405663522}Solution
y = {0, 2.738996856, -0.405663522}
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