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Simplifying 36y3 + 30y2 = 6y4 Reorder the terms: 30y2 + 36y3 = 6y4 Solving 30y2 + 36y3 = 6y4 Solving for variable 'y'. Combine like terms: 6y4 + -6y4 = 0 30y2 + 36y3 + -6y4 = 0 Factor out the Greatest Common Factor (GCF), '6y2'. 6y2(5 + 6y + -1y2) = 0 Ignore the factor 6.Subproblem 1
Set the factor 'y2' equal to zero and attempt to solve: Simplifying y2 = 0 Solving y2 = 0 Move all terms containing y to the left, all other terms to the right. Simplifying y2 = 0 Take the square root of each side: y = {0}Subproblem 2
Set the factor '(5 + 6y + -1y2)' equal to zero and attempt to solve: Simplifying 5 + 6y + -1y2 = 0 Solving 5 + 6y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -5 + -6y + y2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -6y + 5 + y2 = 0 + 5 Reorder the terms: -5 + 5 + -6y + y2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -6y + y2 = 0 + 5 -6y + y2 = 0 + 5 Combine like terms: 0 + 5 = 5 -6y + y2 = 5 The y term is -6y. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6y + 9 + y2 = 5 + 9 Reorder the terms: 9 + -6y + y2 = 5 + 9 Combine like terms: 5 + 9 = 14 9 + -6y + y2 = 14 Factor a perfect square on the left side: (y + -3)(y + -3) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (y + -3) equal to 3.741657387 and -3.741657387.Subproblem 1
y + -3 = 3.741657387 Simplifying y + -3 = 3.741657387 Reorder the terms: -3 + y = 3.741657387 Solving -3 + y = 3.741657387 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + y = 3.741657387 + 3 Combine like terms: -3 + 3 = 0 0 + y = 3.741657387 + 3 y = 3.741657387 + 3 Combine like terms: 3.741657387 + 3 = 6.741657387 y = 6.741657387 Simplifying y = 6.741657387Subproblem 2
y + -3 = -3.741657387 Simplifying y + -3 = -3.741657387 Reorder the terms: -3 + y = -3.741657387 Solving -3 + y = -3.741657387 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + y = -3.741657387 + 3 Combine like terms: -3 + 3 = 0 0 + y = -3.741657387 + 3 y = -3.741657387 + 3 Combine like terms: -3.741657387 + 3 = -0.741657387 y = -0.741657387 Simplifying y = -0.741657387Solution
The solution to the problem is based on the solutions from the subproblems. y = {6.741657387, -0.741657387}Solution
y = {0, 6.741657387, -0.741657387}
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