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Simplifying 4y2 + 11y + -21 = 0 Reorder the terms: -21 + 11y + 4y2 = 0 Solving -21 + 11y + 4y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -5.25 + 2.75y + y2 = 0 Move the constant term to the right: Add '5.25' to each side of the equation. -5.25 + 2.75y + 5.25 + y2 = 0 + 5.25 Reorder the terms: -5.25 + 5.25 + 2.75y + y2 = 0 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + 2.75y + y2 = 0 + 5.25 2.75y + y2 = 0 + 5.25 Combine like terms: 0 + 5.25 = 5.25 2.75y + y2 = 5.25 The y term is 2.75y. Take half its coefficient (1.375). Square it (1.890625) and add it to both sides. Add '1.890625' to each side of the equation. 2.75y + 1.890625 + y2 = 5.25 + 1.890625 Reorder the terms: 1.890625 + 2.75y + y2 = 5.25 + 1.890625 Combine like terms: 5.25 + 1.890625 = 7.140625 1.890625 + 2.75y + y2 = 7.140625 Factor a perfect square on the left side: (y + 1.375)(y + 1.375) = 7.140625 Calculate the square root of the right side: 2.672194791 Break this problem into two subproblems by setting (y + 1.375) equal to 2.672194791 and -2.672194791.Subproblem 1
y + 1.375 = 2.672194791 Simplifying y + 1.375 = 2.672194791 Reorder the terms: 1.375 + y = 2.672194791 Solving 1.375 + y = 2.672194791 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.375' to each side of the equation. 1.375 + -1.375 + y = 2.672194791 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + y = 2.672194791 + -1.375 y = 2.672194791 + -1.375 Combine like terms: 2.672194791 + -1.375 = 1.297194791 y = 1.297194791 Simplifying y = 1.297194791Subproblem 2
y + 1.375 = -2.672194791 Simplifying y + 1.375 = -2.672194791 Reorder the terms: 1.375 + y = -2.672194791 Solving 1.375 + y = -2.672194791 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.375' to each side of the equation. 1.375 + -1.375 + y = -2.672194791 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + y = -2.672194791 + -1.375 y = -2.672194791 + -1.375 Combine like terms: -2.672194791 + -1.375 = -4.047194791 y = -4.047194791 Simplifying y = -4.047194791Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.297194791, -4.047194791}
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