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Simplifying 4x2 + -41x + 21 = 0 Reorder the terms: 21 + -41x + 4x2 = 0 Solving 21 + -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'. 5.25 + -10.25x + x2 = 0 Move the constant term to the right: Add '-5.25' to each side of the equation. 5.25 + -10.25x + -5.25 + x2 = 0 + -5.25 Reorder the terms: 5.25 + -5.25 + -10.25x + x2 = 0 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + -10.25x + x2 = 0 + -5.25 -10.25x + x2 = 0 + -5.25 Combine like terms: 0 + -5.25 = -5.25 -10.25x + x2 = -5.25 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 = -5.25 + 26.265625 Reorder the terms: 26.265625 + -10.25x + x2 = -5.25 + 26.265625 Combine like terms: -5.25 + 26.265625 = 21.015625 26.265625 + -10.25x + x2 = 21.015625 Factor a perfect square on the left side: (x + -5.125)(x + -5.125) = 21.015625 Calculate the square root of the right side: 4.584280205 Break this problem into two subproblems by setting (x + -5.125) equal to 4.584280205 and -4.584280205.Subproblem 1
x + -5.125 = 4.584280205 Simplifying x + -5.125 = 4.584280205 Reorder the terms: -5.125 + x = 4.584280205 Solving -5.125 + x = 4.584280205 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 = 4.584280205 + 5.125 Combine like terms: -5.125 + 5.125 = 0.000 0.000 + x = 4.584280205 + 5.125 x = 4.584280205 + 5.125 Combine like terms: 4.584280205 + 5.125 = 9.709280205 x = 9.709280205 Simplifying x = 9.709280205Subproblem 2
x + -5.125 = -4.584280205 Simplifying x + -5.125 = -4.584280205 Reorder the terms: -5.125 + x = -4.584280205 Solving -5.125 + x = -4.584280205 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 = -4.584280205 + 5.125 Combine like terms: -5.125 + 5.125 = 0.000 0.000 + x = -4.584280205 + 5.125 x = -4.584280205 + 5.125 Combine like terms: -4.584280205 + 5.125 = 0.540719795 x = 0.540719795 Simplifying x = 0.540719795Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.709280205, 0.540719795}
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