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Simplifying 0 = 2y2 + -24y + -72 Reorder the terms: 0 = -72 + -24y + 2y2 Solving 0 = -72 + -24y + 2y2 Solving for variable 'y'. Combine like terms: 0 + 72 = 72 72 + 24y + -2y2 = -72 + -24y + 2y2 + 72 + 24y + -2y2 Reorder the terms: 72 + 24y + -2y2 = -72 + 72 + -24y + 24y + 2y2 + -2y2 Combine like terms: -72 + 72 = 0 72 + 24y + -2y2 = 0 + -24y + 24y + 2y2 + -2y2 72 + 24y + -2y2 = -24y + 24y + 2y2 + -2y2 Combine like terms: -24y + 24y = 0 72 + 24y + -2y2 = 0 + 2y2 + -2y2 72 + 24y + -2y2 = 2y2 + -2y2 Combine like terms: 2y2 + -2y2 = 0 72 + 24y + -2y2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(36 + 12y + -1y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(36 + 12y + -1y2)' equal to zero and attempt to solve: Simplifying 36 + 12y + -1y2 = 0 Solving 36 + 12y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -36 + -12y + y2 = 0 Move the constant term to the right: Add '36' to each side of the equation. -36 + -12y + 36 + y2 = 0 + 36 Reorder the terms: -36 + 36 + -12y + y2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -12y + y2 = 0 + 36 -12y + y2 = 0 + 36 Combine like terms: 0 + 36 = 36 -12y + y2 = 36 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 = 36 + 36 Reorder the terms: 36 + -12y + y2 = 36 + 36 Combine like terms: 36 + 36 = 72 36 + -12y + y2 = 72 Factor a perfect square on the left side: (y + -6)(y + -6) = 72 Calculate the square root of the right side: 8.485281374 Break this problem into two subproblems by setting (y + -6) equal to 8.485281374 and -8.485281374.Subproblem 1
y + -6 = 8.485281374 Simplifying y + -6 = 8.485281374 Reorder the terms: -6 + y = 8.485281374 Solving -6 + y = 8.485281374 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 = 8.485281374 + 6 Combine like terms: -6 + 6 = 0 0 + y = 8.485281374 + 6 y = 8.485281374 + 6 Combine like terms: 8.485281374 + 6 = 14.485281374 y = 14.485281374 Simplifying y = 14.485281374Subproblem 2
y + -6 = -8.485281374 Simplifying y + -6 = -8.485281374 Reorder the terms: -6 + y = -8.485281374 Solving -6 + y = -8.485281374 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 = -8.485281374 + 6 Combine like terms: -6 + 6 = 0 0 + y = -8.485281374 + 6 y = -8.485281374 + 6 Combine like terms: -8.485281374 + 6 = -2.485281374 y = -2.485281374 Simplifying y = -2.485281374Solution
The solution to the problem is based on the solutions from the subproblems. y = {14.485281374, -2.485281374}Solution
y = {14.485281374, -2.485281374}
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