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Simplifying (9y)(81 + 9y + -1y2) = 0 Remove parenthesis around (9y) 9y(81 + 9y + -1y2) = 0 (81 * 9y + 9y * 9y + -1y2 * 9y) = 0 (729y + 81y2 + -9y3) = 0 Solving 729y + 81y2 + -9y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '9y'. 9y(81 + 9y + -1y2) = 0 Ignore the factor 9.Subproblem 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 '(81 + 9y + -1y2)' equal to zero and attempt to solve: Simplifying 81 + 9y + -1y2 = 0 Solving 81 + 9y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -81 + -9y + y2 = 0 Move the constant term to the right: Add '81' to each side of the equation. -81 + -9y + 81 + y2 = 0 + 81 Reorder the terms: -81 + 81 + -9y + y2 = 0 + 81 Combine like terms: -81 + 81 = 0 0 + -9y + y2 = 0 + 81 -9y + y2 = 0 + 81 Combine like terms: 0 + 81 = 81 -9y + y2 = 81 The y term is -9y. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9y + 20.25 + y2 = 81 + 20.25 Reorder the terms: 20.25 + -9y + y2 = 81 + 20.25 Combine like terms: 81 + 20.25 = 101.25 20.25 + -9y + y2 = 101.25 Factor a perfect square on the left side: (y + -4.5)(y + -4.5) = 101.25 Calculate the square root of the right side: 10.062305899 Break this problem into two subproblems by setting (y + -4.5) equal to 10.062305899 and -10.062305899.Subproblem 1
y + -4.5 = 10.062305899 Simplifying y + -4.5 = 10.062305899 Reorder the terms: -4.5 + y = 10.062305899 Solving -4.5 + y = 10.062305899 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + y = 10.062305899 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + y = 10.062305899 + 4.5 y = 10.062305899 + 4.5 Combine like terms: 10.062305899 + 4.5 = 14.562305899 y = 14.562305899 Simplifying y = 14.562305899Subproblem 2
y + -4.5 = -10.062305899 Simplifying y + -4.5 = -10.062305899 Reorder the terms: -4.5 + y = -10.062305899 Solving -4.5 + y = -10.062305899 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + y = -10.062305899 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + y = -10.062305899 + 4.5 y = -10.062305899 + 4.5 Combine like terms: -10.062305899 + 4.5 = -5.562305899 y = -5.562305899 Simplifying y = -5.562305899Solution
The solution to the problem is based on the solutions from the subproblems. y = {14.562305899, -5.562305899}Solution
y = {0, 14.562305899, -5.562305899}
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