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Simplifying 38y + y2 = 24 Solving 38y + y2 = 24 Solving for variable 'y'. Reorder the terms: -24 + 38y + y2 = 24 + -24 Combine like terms: 24 + -24 = 0 -24 + 38y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '24' to each side of the equation. -24 + 38y + 24 + y2 = 0 + 24 Reorder the terms: -24 + 24 + 38y + y2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + 38y + y2 = 0 + 24 38y + y2 = 0 + 24 Combine like terms: 0 + 24 = 24 38y + y2 = 24 The y term is 38y. Take half its coefficient (19). Square it (361) and add it to both sides. Add '361' to each side of the equation. 38y + 361 + y2 = 24 + 361 Reorder the terms: 361 + 38y + y2 = 24 + 361 Combine like terms: 24 + 361 = 385 361 + 38y + y2 = 385 Factor a perfect square on the left side: (y + 19)(y + 19) = 385 Calculate the square root of the right side: 19.62141687 Break this problem into two subproblems by setting (y + 19) equal to 19.62141687 and -19.62141687.Subproblem 1
y + 19 = 19.62141687 Simplifying y + 19 = 19.62141687 Reorder the terms: 19 + y = 19.62141687 Solving 19 + y = 19.62141687 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-19' to each side of the equation. 19 + -19 + y = 19.62141687 + -19 Combine like terms: 19 + -19 = 0 0 + y = 19.62141687 + -19 y = 19.62141687 + -19 Combine like terms: 19.62141687 + -19 = 0.62141687 y = 0.62141687 Simplifying y = 0.62141687Subproblem 2
y + 19 = -19.62141687 Simplifying y + 19 = -19.62141687 Reorder the terms: 19 + y = -19.62141687 Solving 19 + y = -19.62141687 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-19' to each side of the equation. 19 + -19 + y = -19.62141687 + -19 Combine like terms: 19 + -19 = 0 0 + y = -19.62141687 + -19 y = -19.62141687 + -19 Combine like terms: -19.62141687 + -19 = -38.62141687 y = -38.62141687 Simplifying y = -38.62141687Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.62141687, -38.62141687}
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