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Simplifying y2 = 24 + -6y Solving y2 = 24 + -6y Solving for variable 'y'. Reorder the terms: -24 + 6y + y2 = 24 + -6y + -24 + 6y Reorder the terms: -24 + 6y + y2 = 24 + -24 + -6y + 6y Combine like terms: 24 + -24 = 0 -24 + 6y + y2 = 0 + -6y + 6y -24 + 6y + y2 = -6y + 6y Combine like terms: -6y + 6y = 0 -24 + 6y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '24' to each side of the equation. -24 + 6y + 24 + y2 = 0 + 24 Reorder the terms: -24 + 24 + 6y + y2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + 6y + y2 = 0 + 24 6y + y2 = 0 + 24 Combine like terms: 0 + 24 = 24 6y + y2 = 24 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 = 24 + 9 Reorder the terms: 9 + 6y + y2 = 24 + 9 Combine like terms: 24 + 9 = 33 9 + 6y + y2 = 33 Factor a perfect square on the left side: (y + 3)(y + 3) = 33 Calculate the square root of the right side: 5.744562647 Break this problem into two subproblems by setting (y + 3) equal to 5.744562647 and -5.744562647.Subproblem 1
y + 3 = 5.744562647 Simplifying y + 3 = 5.744562647 Reorder the terms: 3 + y = 5.744562647 Solving 3 + y = 5.744562647 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 = 5.744562647 + -3 Combine like terms: 3 + -3 = 0 0 + y = 5.744562647 + -3 y = 5.744562647 + -3 Combine like terms: 5.744562647 + -3 = 2.744562647 y = 2.744562647 Simplifying y = 2.744562647Subproblem 2
y + 3 = -5.744562647 Simplifying y + 3 = -5.744562647 Reorder the terms: 3 + y = -5.744562647 Solving 3 + y = -5.744562647 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 = -5.744562647 + -3 Combine like terms: 3 + -3 = 0 0 + y = -5.744562647 + -3 y = -5.744562647 + -3 Combine like terms: -5.744562647 + -3 = -8.744562647 y = -8.744562647 Simplifying y = -8.744562647Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.744562647, -8.744562647}
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