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Simplifying 4x2 + -41x + -82 = 0 Reorder the terms: -82 + -41x + 4x2 = 0 Solving -82 + -41x + 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'. -20.5 + -10.25x + x2 = 0 Move the constant term to the right: Add '20.5' to each side of the equation. -20.5 + -10.25x + 20.5 + x2 = 0 + 20.5 Reorder the terms: -20.5 + 20.5 + -10.25x + x2 = 0 + 20.5 Combine like terms: -20.5 + 20.5 = 0.0 0.0 + -10.25x + x2 = 0 + 20.5 -10.25x + x2 = 0 + 20.5 Combine like terms: 0 + 20.5 = 20.5 -10.25x + x2 = 20.5 The x term is -10.25x. Take half its coefficient (-5.125). Square it (26.265625) and add it to both sides. Add '26.265625' to each side of the equation. -10.25x + 26.265625 + x2 = 20.5 + 26.265625 Reorder the terms: 26.265625 + -10.25x + x2 = 20.5 + 26.265625 Combine like terms: 20.5 + 26.265625 = 46.765625 26.265625 + -10.25x + x2 = 46.765625 Factor a perfect square on the left side: (x + -5.125)(x + -5.125) = 46.765625 Calculate the square root of the right side: 6.838539683 Break this problem into two subproblems by setting (x + -5.125) equal to 6.838539683 and -6.838539683.Subproblem 1
x + -5.125 = 6.838539683 Simplifying x + -5.125 = 6.838539683 Reorder the terms: -5.125 + x = 6.838539683 Solving -5.125 + x = 6.838539683 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.125' to each side of the equation. -5.125 + 5.125 + x = 6.838539683 + 5.125 Combine like terms: -5.125 + 5.125 = 0.000 0.000 + x = 6.838539683 + 5.125 x = 6.838539683 + 5.125 Combine like terms: 6.838539683 + 5.125 = 11.963539683 x = 11.963539683 Simplifying x = 11.963539683Subproblem 2
x + -5.125 = -6.838539683 Simplifying x + -5.125 = -6.838539683 Reorder the terms: -5.125 + x = -6.838539683 Solving -5.125 + x = -6.838539683 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.125' to each side of the equation. -5.125 + 5.125 + x = -6.838539683 + 5.125 Combine like terms: -5.125 + 5.125 = 0.000 0.000 + x = -6.838539683 + 5.125 x = -6.838539683 + 5.125 Combine like terms: -6.838539683 + 5.125 = -1.713539683 x = -1.713539683 Simplifying x = -1.713539683Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.963539683, -1.713539683}
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