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Simplifying y2 + 38y + 21 = 0 Reorder the terms: 21 + 38y + y2 = 0 Solving 21 + 38y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-21' to each side of the equation. 21 + 38y + -21 + y2 = 0 + -21 Reorder the terms: 21 + -21 + 38y + y2 = 0 + -21 Combine like terms: 21 + -21 = 0 0 + 38y + y2 = 0 + -21 38y + y2 = 0 + -21 Combine like terms: 0 + -21 = -21 38y + y2 = -21 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 = -21 + 361 Reorder the terms: 361 + 38y + y2 = -21 + 361 Combine like terms: -21 + 361 = 340 361 + 38y + y2 = 340 Factor a perfect square on the left side: (y + 19)(y + 19) = 340 Calculate the square root of the right side: 18.439088915 Break this problem into two subproblems by setting (y + 19) equal to 18.439088915 and -18.439088915.Subproblem 1
y + 19 = 18.439088915 Simplifying y + 19 = 18.439088915 Reorder the terms: 19 + y = 18.439088915 Solving 19 + y = 18.439088915 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 = 18.439088915 + -19 Combine like terms: 19 + -19 = 0 0 + y = 18.439088915 + -19 y = 18.439088915 + -19 Combine like terms: 18.439088915 + -19 = -0.560911085 y = -0.560911085 Simplifying y = -0.560911085Subproblem 2
y + 19 = -18.439088915 Simplifying y + 19 = -18.439088915 Reorder the terms: 19 + y = -18.439088915 Solving 19 + y = -18.439088915 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 = -18.439088915 + -19 Combine like terms: 19 + -19 = 0 0 + y = -18.439088915 + -19 y = -18.439088915 + -19 Combine like terms: -18.439088915 + -19 = -37.439088915 y = -37.439088915 Simplifying y = -37.439088915Solution
The solution to the problem is based on the solutions from the subproblems. y = {-0.560911085, -37.439088915}
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