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Simplifying 24 = y2 + 2y + -15 Reorder the terms: 24 = -15 + 2y + y2 Solving 24 = -15 + 2y + y2 Solving for variable 'y'. Combine like terms: 24 + 15 = 39 39 + -2y + -1y2 = -15 + 2y + y2 + 15 + -2y + -1y2 Reorder the terms: 39 + -2y + -1y2 = -15 + 15 + 2y + -2y + y2 + -1y2 Combine like terms: -15 + 15 = 0 39 + -2y + -1y2 = 0 + 2y + -2y + y2 + -1y2 39 + -2y + -1y2 = 2y + -2y + y2 + -1y2 Combine like terms: 2y + -2y = 0 39 + -2y + -1y2 = 0 + y2 + -1y2 39 + -2y + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 39 + -2y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -39 + 2y + y2 = 0 Move the constant term to the right: Add '39' to each side of the equation. -39 + 2y + 39 + y2 = 0 + 39 Reorder the terms: -39 + 39 + 2y + y2 = 0 + 39 Combine like terms: -39 + 39 = 0 0 + 2y + y2 = 0 + 39 2y + y2 = 0 + 39 Combine like terms: 0 + 39 = 39 2y + y2 = 39 The y term is 2y. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2y + 1 + y2 = 39 + 1 Reorder the terms: 1 + 2y + y2 = 39 + 1 Combine like terms: 39 + 1 = 40 1 + 2y + y2 = 40 Factor a perfect square on the left side: (y + 1)(y + 1) = 40 Calculate the square root of the right side: 6.32455532 Break this problem into two subproblems by setting (y + 1) equal to 6.32455532 and -6.32455532.Subproblem 1
y + 1 = 6.32455532 Simplifying y + 1 = 6.32455532 Reorder the terms: 1 + y = 6.32455532 Solving 1 + y = 6.32455532 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y = 6.32455532 + -1 Combine like terms: 1 + -1 = 0 0 + y = 6.32455532 + -1 y = 6.32455532 + -1 Combine like terms: 6.32455532 + -1 = 5.32455532 y = 5.32455532 Simplifying y = 5.32455532Subproblem 2
y + 1 = -6.32455532 Simplifying y + 1 = -6.32455532 Reorder the terms: 1 + y = -6.32455532 Solving 1 + y = -6.32455532 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y = -6.32455532 + -1 Combine like terms: 1 + -1 = 0 0 + y = -6.32455532 + -1 y = -6.32455532 + -1 Combine like terms: -6.32455532 + -1 = -7.32455532 y = -7.32455532 Simplifying y = -7.32455532Solution
The solution to the problem is based on the solutions from the subproblems. y = {5.32455532, -7.32455532}
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