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Simplifying 15y2(y2 + -12y + -24) = 0 Reorder the terms: 15y2(-24 + -12y + y2) = 0 (-24 * 15y2 + -12y * 15y2 + y2 * 15y2) = 0 (-360y2 + -180y3 + 15y4) = 0 Solving -360y2 + -180y3 + 15y4 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '15y2'. 15y2(-24 + -12y + y2) = 0 Ignore the factor 15.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 '(-24 + -12y + y2)' equal to zero and attempt to solve: Simplifying -24 + -12y + y2 = 0 Solving -24 + -12y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '24' to each side of the equation. -24 + -12y + 24 + y2 = 0 + 24 Reorder the terms: -24 + 24 + -12y + y2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -12y + y2 = 0 + 24 -12y + y2 = 0 + 24 Combine like terms: 0 + 24 = 24 -12y + y2 = 24 The y term is -12y. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12y + 36 + y2 = 24 + 36 Reorder the terms: 36 + -12y + y2 = 24 + 36 Combine like terms: 24 + 36 = 60 36 + -12y + y2 = 60 Factor a perfect square on the left side: (y + -6)(y + -6) = 60 Calculate the square root of the right side: 7.745966692 Break this problem into two subproblems by setting (y + -6) equal to 7.745966692 and -7.745966692.Subproblem 1
y + -6 = 7.745966692 Simplifying y + -6 = 7.745966692 Reorder the terms: -6 + y = 7.745966692 Solving -6 + y = 7.745966692 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + y = 7.745966692 + 6 Combine like terms: -6 + 6 = 0 0 + y = 7.745966692 + 6 y = 7.745966692 + 6 Combine like terms: 7.745966692 + 6 = 13.745966692 y = 13.745966692 Simplifying y = 13.745966692Subproblem 2
y + -6 = -7.745966692 Simplifying y + -6 = -7.745966692 Reorder the terms: -6 + y = -7.745966692 Solving -6 + y = -7.745966692 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + y = -7.745966692 + 6 Combine like terms: -6 + 6 = 0 0 + y = -7.745966692 + 6 y = -7.745966692 + 6 Combine like terms: -7.745966692 + 6 = -1.745966692 y = -1.745966692 Simplifying y = -1.745966692Solution
The solution to the problem is based on the solutions from the subproblems. y = {13.745966692, -1.745966692}Solution
y = {0, 13.745966692, -1.745966692}
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