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Simplifying 4x2 + -67x + -254 = 0 Reorder the terms: -254 + -67x + 4x2 = 0 Solving -254 + -67x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -63.5 + -16.75x + x2 = 0 Move the constant term to the right: Add '63.5' to each side of the equation. -63.5 + -16.75x + 63.5 + x2 = 0 + 63.5 Reorder the terms: -63.5 + 63.5 + -16.75x + x2 = 0 + 63.5 Combine like terms: -63.5 + 63.5 = 0.0 0.0 + -16.75x + x2 = 0 + 63.5 -16.75x + x2 = 0 + 63.5 Combine like terms: 0 + 63.5 = 63.5 -16.75x + x2 = 63.5 The x term is -16.75x. Take half its coefficient (-8.375). Square it (70.140625) and add it to both sides. Add '70.140625' to each side of the equation. -16.75x + 70.140625 + x2 = 63.5 + 70.140625 Reorder the terms: 70.140625 + -16.75x + x2 = 63.5 + 70.140625 Combine like terms: 63.5 + 70.140625 = 133.640625 70.140625 + -16.75x + x2 = 133.640625 Factor a perfect square on the left side: (x + -8.375)(x + -8.375) = 133.640625 Calculate the square root of the right side: 11.560303845 Break this problem into two subproblems by setting (x + -8.375) equal to 11.560303845 and -11.560303845.Subproblem 1
x + -8.375 = 11.560303845 Simplifying x + -8.375 = 11.560303845 Reorder the terms: -8.375 + x = 11.560303845 Solving -8.375 + x = 11.560303845 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.375' to each side of the equation. -8.375 + 8.375 + x = 11.560303845 + 8.375 Combine like terms: -8.375 + 8.375 = 0.000 0.000 + x = 11.560303845 + 8.375 x = 11.560303845 + 8.375 Combine like terms: 11.560303845 + 8.375 = 19.935303845 x = 19.935303845 Simplifying x = 19.935303845Subproblem 2
x + -8.375 = -11.560303845 Simplifying x + -8.375 = -11.560303845 Reorder the terms: -8.375 + x = -11.560303845 Solving -8.375 + x = -11.560303845 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.375' to each side of the equation. -8.375 + 8.375 + x = -11.560303845 + 8.375 Combine like terms: -8.375 + 8.375 = 0.000 0.000 + x = -11.560303845 + 8.375 x = -11.560303845 + 8.375 Combine like terms: -11.560303845 + 8.375 = -3.185303845 x = -3.185303845 Simplifying x = -3.185303845Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.935303845, -3.185303845}
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