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Simplifying 3y2 + 18y = 15 Reorder the terms: 18y + 3y2 = 15 Solving 18y + 3y2 = 15 Solving for variable 'y'. Reorder the terms: -15 + 18y + 3y2 = 15 + -15 Combine like terms: 15 + -15 = 0 -15 + 18y + 3y2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-5 + 6y + y2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-5 + 6y + y2)' equal to zero and attempt to solve: Simplifying -5 + 6y + y2 = 0 Solving -5 + 6y + y2 = 0 Begin completing the square. 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 = 0.741657387 y = 0.741657387 Simplifying y = 0.741657387Subproblem 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 = -6.741657387 y = -6.741657387 Simplifying y = -6.741657387Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.741657387, -6.741657387}Solution
y = {0.741657387, -6.741657387}
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