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Simplifying 4x2 = 11x + 21 Reorder the terms: 4x2 = 21 + 11x Solving 4x2 = 21 + 11x Solving for variable 'x'. Reorder the terms: -21 + -11x + 4x2 = 21 + 11x + -21 + -11x Reorder the terms: -21 + -11x + 4x2 = 21 + -21 + 11x + -11x Combine like terms: 21 + -21 = 0 -21 + -11x + 4x2 = 0 + 11x + -11x -21 + -11x + 4x2 = 11x + -11x Combine like terms: 11x + -11x = 0 -21 + -11x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -5.25 + -2.75x + x2 = 0 Move the constant term to the right: Add '5.25' to each side of the equation. -5.25 + -2.75x + 5.25 + x2 = 0 + 5.25 Reorder the terms: -5.25 + 5.25 + -2.75x + x2 = 0 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + -2.75x + x2 = 0 + 5.25 -2.75x + x2 = 0 + 5.25 Combine like terms: 0 + 5.25 = 5.25 -2.75x + x2 = 5.25 The x term is -2.75x. 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. -2.75x + 1.890625 + x2 = 5.25 + 1.890625 Reorder the terms: 1.890625 + -2.75x + x2 = 5.25 + 1.890625 Combine like terms: 5.25 + 1.890625 = 7.140625 1.890625 + -2.75x + x2 = 7.140625 Factor a perfect square on the left side: (x + -1.375)(x + -1.375) = 7.140625 Calculate the square root of the right side: 2.672194791 Break this problem into two subproblems by setting (x + -1.375) equal to 2.672194791 and -2.672194791.Subproblem 1
x + -1.375 = 2.672194791 Simplifying x + -1.375 = 2.672194791 Reorder the terms: -1.375 + x = 2.672194791 Solving -1.375 + x = 2.672194791 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + x = 2.672194791 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = 2.672194791 + 1.375 x = 2.672194791 + 1.375 Combine like terms: 2.672194791 + 1.375 = 4.047194791 x = 4.047194791 Simplifying x = 4.047194791Subproblem 2
x + -1.375 = -2.672194791 Simplifying x + -1.375 = -2.672194791 Reorder the terms: -1.375 + x = -2.672194791 Solving -1.375 + x = -2.672194791 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + x = -2.672194791 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = -2.672194791 + 1.375 x = -2.672194791 + 1.375 Combine like terms: -2.672194791 + 1.375 = -1.297194791 x = -1.297194791 Simplifying x = -1.297194791Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.047194791, -1.297194791}
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