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Simplifying 15y3 + -55y2 + 3y = 0 Reorder the terms: 3y + -55y2 + 15y3 = 0 Solving 3y + -55y2 + 15y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), 'y'. y(3 + -55y + 15y2) = 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 '(3 + -55y + 15y2)' equal to zero and attempt to solve: Simplifying 3 + -55y + 15y2 = 0 Solving 3 + -55y + 15y2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. 0.2 + -3.666666667y + y2 = 0 Move the constant term to the right: Add '-0.2' to each side of the equation. 0.2 + -3.666666667y + -0.2 + y2 = 0 + -0.2 Reorder the terms: 0.2 + -0.2 + -3.666666667y + y2 = 0 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + -3.666666667y + y2 = 0 + -0.2 -3.666666667y + y2 = 0 + -0.2 Combine like terms: 0 + -0.2 = -0.2 -3.666666667y + y2 = -0.2 The y term is -3.666666667y. Take half its coefficient (-1.833333334). Square it (3.361111114) and add it to both sides. Add '3.361111114' to each side of the equation. -3.666666667y + 3.361111114 + y2 = -0.2 + 3.361111114 Reorder the terms: 3.361111114 + -3.666666667y + y2 = -0.2 + 3.361111114 Combine like terms: -0.2 + 3.361111114 = 3.161111114 3.361111114 + -3.666666667y + y2 = 3.161111114 Factor a perfect square on the left side: (y + -1.833333334)(y + -1.833333334) = 3.161111114 Calculate the square root of the right side: 1.777951381 Break this problem into two subproblems by setting (y + -1.833333334) equal to 1.777951381 and -1.777951381.Subproblem 1
y + -1.833333334 = 1.777951381 Simplifying y + -1.833333334 = 1.777951381 Reorder the terms: -1.833333334 + y = 1.777951381 Solving -1.833333334 + y = 1.777951381 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.833333334' to each side of the equation. -1.833333334 + 1.833333334 + y = 1.777951381 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + y = 1.777951381 + 1.833333334 y = 1.777951381 + 1.833333334 Combine like terms: 1.777951381 + 1.833333334 = 3.611284715 y = 3.611284715 Simplifying y = 3.611284715Subproblem 2
y + -1.833333334 = -1.777951381 Simplifying y + -1.833333334 = -1.777951381 Reorder the terms: -1.833333334 + y = -1.777951381 Solving -1.833333334 + y = -1.777951381 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.833333334' to each side of the equation. -1.833333334 + 1.833333334 + y = -1.777951381 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + y = -1.777951381 + 1.833333334 y = -1.777951381 + 1.833333334 Combine like terms: -1.777951381 + 1.833333334 = 0.055381953 y = 0.055381953 Simplifying y = 0.055381953Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.611284715, 0.055381953}Solution
y = {0, 3.611284715, 0.055381953}
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