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Simplifying 9y2 + -216y + -432 = 0 Reorder the terms: -432 + -216y + 9y2 = 0 Solving -432 + -216y + 9y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '9'. 9(-48 + -24y + y2) = 0 Ignore the factor 9.Subproblem 1
Set the factor '(-48 + -24y + y2)' equal to zero and attempt to solve: Simplifying -48 + -24y + y2 = 0 Solving -48 + -24y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '48' to each side of the equation. -48 + -24y + 48 + y2 = 0 + 48 Reorder the terms: -48 + 48 + -24y + y2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + -24y + y2 = 0 + 48 -24y + y2 = 0 + 48 Combine like terms: 0 + 48 = 48 -24y + y2 = 48 The y term is -24y. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24y + 144 + y2 = 48 + 144 Reorder the terms: 144 + -24y + y2 = 48 + 144 Combine like terms: 48 + 144 = 192 144 + -24y + y2 = 192 Factor a perfect square on the left side: (y + -12)(y + -12) = 192 Calculate the square root of the right side: 13.856406461 Break this problem into two subproblems by setting (y + -12) equal to 13.856406461 and -13.856406461.Subproblem 1
y + -12 = 13.856406461 Simplifying y + -12 = 13.856406461 Reorder the terms: -12 + y = 13.856406461 Solving -12 + y = 13.856406461 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + y = 13.856406461 + 12 Combine like terms: -12 + 12 = 0 0 + y = 13.856406461 + 12 y = 13.856406461 + 12 Combine like terms: 13.856406461 + 12 = 25.856406461 y = 25.856406461 Simplifying y = 25.856406461Subproblem 2
y + -12 = -13.856406461 Simplifying y + -12 = -13.856406461 Reorder the terms: -12 + y = -13.856406461 Solving -12 + y = -13.856406461 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + y = -13.856406461 + 12 Combine like terms: -12 + 12 = 0 0 + y = -13.856406461 + 12 y = -13.856406461 + 12 Combine like terms: -13.856406461 + 12 = -1.856406461 y = -1.856406461 Simplifying y = -1.856406461Solution
The solution to the problem is based on the solutions from the subproblems. y = {25.856406461, -1.856406461}Solution
y = {25.856406461, -1.856406461}
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