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Simplifying 4y3 + -18y2 + 16y = 0 Reorder the terms: 16y + -18y2 + 4y3 = 0 Solving 16y + -18y2 + 4y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2y'. 2y(8 + -9y + 2y2) = 0 Ignore the factor 2.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 '(8 + -9y + 2y2)' equal to zero and attempt to solve: Simplifying 8 + -9y + 2y2 = 0 Solving 8 + -9y + 2y2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 4 + -4.5y + y2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -4.5y + -4 + y2 = 0 + -4 Reorder the terms: 4 + -4 + -4.5y + y2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -4.5y + y2 = 0 + -4 -4.5y + y2 = 0 + -4 Combine like terms: 0 + -4 = -4 -4.5y + y2 = -4 The y term is -4.5y. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5y + 5.0625 + y2 = -4 + 5.0625 Reorder the terms: 5.0625 + -4.5y + y2 = -4 + 5.0625 Combine like terms: -4 + 5.0625 = 1.0625 5.0625 + -4.5y + y2 = 1.0625 Factor a perfect square on the left side: (y + -2.25)(y + -2.25) = 1.0625 Calculate the square root of the right side: 1.030776406 Break this problem into two subproblems by setting (y + -2.25) equal to 1.030776406 and -1.030776406.Subproblem 1
y + -2.25 = 1.030776406 Simplifying y + -2.25 = 1.030776406 Reorder the terms: -2.25 + y = 1.030776406 Solving -2.25 + y = 1.030776406 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + y = 1.030776406 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + y = 1.030776406 + 2.25 y = 1.030776406 + 2.25 Combine like terms: 1.030776406 + 2.25 = 3.280776406 y = 3.280776406 Simplifying y = 3.280776406Subproblem 2
y + -2.25 = -1.030776406 Simplifying y + -2.25 = -1.030776406 Reorder the terms: -2.25 + y = -1.030776406 Solving -2.25 + y = -1.030776406 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + y = -1.030776406 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + y = -1.030776406 + 2.25 y = -1.030776406 + 2.25 Combine like terms: -1.030776406 + 2.25 = 1.219223594 y = 1.219223594 Simplifying y = 1.219223594Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.280776406, 1.219223594}Solution
y = {0, 3.280776406, 1.219223594}
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