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Simplifying 2y + y2 = 420 Solving 2y + y2 = 420 Solving for variable 'y'. Reorder the terms: -420 + 2y + y2 = 420 + -420 Combine like terms: 420 + -420 = 0 -420 + 2y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '420' to each side of the equation. -420 + 2y + 420 + y2 = 0 + 420 Reorder the terms: -420 + 420 + 2y + y2 = 0 + 420 Combine like terms: -420 + 420 = 0 0 + 2y + y2 = 0 + 420 2y + y2 = 0 + 420 Combine like terms: 0 + 420 = 420 2y + y2 = 420 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 = 420 + 1 Reorder the terms: 1 + 2y + y2 = 420 + 1 Combine like terms: 420 + 1 = 421 1 + 2y + y2 = 421 Factor a perfect square on the left side: (y + 1)(y + 1) = 421 Calculate the square root of the right side: 20.518284529 Break this problem into two subproblems by setting (y + 1) equal to 20.518284529 and -20.518284529.Subproblem 1
y + 1 = 20.518284529 Simplifying y + 1 = 20.518284529 Reorder the terms: 1 + y = 20.518284529 Solving 1 + y = 20.518284529 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 = 20.518284529 + -1 Combine like terms: 1 + -1 = 0 0 + y = 20.518284529 + -1 y = 20.518284529 + -1 Combine like terms: 20.518284529 + -1 = 19.518284529 y = 19.518284529 Simplifying y = 19.518284529Subproblem 2
y + 1 = -20.518284529 Simplifying y + 1 = -20.518284529 Reorder the terms: 1 + y = -20.518284529 Solving 1 + y = -20.518284529 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 = -20.518284529 + -1 Combine like terms: 1 + -1 = 0 0 + y = -20.518284529 + -1 y = -20.518284529 + -1 Combine like terms: -20.518284529 + -1 = -21.518284529 y = -21.518284529 Simplifying y = -21.518284529Solution
The solution to the problem is based on the solutions from the subproblems. y = {19.518284529, -21.518284529}
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