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Simplifying 4x2 + -41x + 71 = 0 Reorder the terms: 71 + -41x + 4x2 = 0 Solving 71 + -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'. 17.75 + -10.25x + x2 = 0 Move the constant term to the right: Add '-17.75' to each side of the equation. 17.75 + -10.25x + -17.75 + x2 = 0 + -17.75 Reorder the terms: 17.75 + -17.75 + -10.25x + x2 = 0 + -17.75 Combine like terms: 17.75 + -17.75 = 0.00 0.00 + -10.25x + x2 = 0 + -17.75 -10.25x + x2 = 0 + -17.75 Combine like terms: 0 + -17.75 = -17.75 -10.25x + x2 = -17.75 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 = -17.75 + 26.265625 Reorder the terms: 26.265625 + -10.25x + x2 = -17.75 + 26.265625 Combine like terms: -17.75 + 26.265625 = 8.515625 26.265625 + -10.25x + x2 = 8.515625 Factor a perfect square on the left side: (x + -5.125)(x + -5.125) = 8.515625 Calculate the square root of the right side: 2.918154382 Break this problem into two subproblems by setting (x + -5.125) equal to 2.918154382 and -2.918154382.Subproblem 1
x + -5.125 = 2.918154382 Simplifying x + -5.125 = 2.918154382 Reorder the terms: -5.125 + x = 2.918154382 Solving -5.125 + x = 2.918154382 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 = 2.918154382 + 5.125 Combine like terms: -5.125 + 5.125 = 0.000 0.000 + x = 2.918154382 + 5.125 x = 2.918154382 + 5.125 Combine like terms: 2.918154382 + 5.125 = 8.043154382 x = 8.043154382 Simplifying x = 8.043154382Subproblem 2
x + -5.125 = -2.918154382 Simplifying x + -5.125 = -2.918154382 Reorder the terms: -5.125 + x = -2.918154382 Solving -5.125 + x = -2.918154382 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 = -2.918154382 + 5.125 Combine like terms: -5.125 + 5.125 = 0.000 0.000 + x = -2.918154382 + 5.125 x = -2.918154382 + 5.125 Combine like terms: -2.918154382 + 5.125 = 2.206845618 x = 2.206845618 Simplifying x = 2.206845618Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.043154382, 2.206845618}
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