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Simplifying 19x2 + -47x + 11 = 0 Reorder the terms: 11 + -47x + 19x2 = 0 Solving 11 + -47x + 19x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 19 the coefficient of the squared term: Divide each side by '19'. 0.5789473684 + -2.473684211x + x2 = 0 Move the constant term to the right: Add '-0.5789473684' to each side of the equation. 0.5789473684 + -2.473684211x + -0.5789473684 + x2 = 0 + -0.5789473684 Reorder the terms: 0.5789473684 + -0.5789473684 + -2.473684211x + x2 = 0 + -0.5789473684 Combine like terms: 0.5789473684 + -0.5789473684 = 0.0000000000 0.0000000000 + -2.473684211x + x2 = 0 + -0.5789473684 -2.473684211x + x2 = 0 + -0.5789473684 Combine like terms: 0 + -0.5789473684 = -0.5789473684 -2.473684211x + x2 = -0.5789473684 The x term is -2.473684211x. Take half its coefficient (-1.236842106). Square it (1.529778395) and add it to both sides. Add '1.529778395' to each side of the equation. -2.473684211x + 1.529778395 + x2 = -0.5789473684 + 1.529778395 Reorder the terms: 1.529778395 + -2.473684211x + x2 = -0.5789473684 + 1.529778395 Combine like terms: -0.5789473684 + 1.529778395 = 0.9508310266 1.529778395 + -2.473684211x + x2 = 0.9508310266 Factor a perfect square on the left side: (x + -1.236842106)(x + -1.236842106) = 0.9508310266 Calculate the square root of the right side: 0.975105649 Break this problem into two subproblems by setting (x + -1.236842106) equal to 0.975105649 and -0.975105649.Subproblem 1
x + -1.236842106 = 0.975105649 Simplifying x + -1.236842106 = 0.975105649 Reorder the terms: -1.236842106 + x = 0.975105649 Solving -1.236842106 + x = 0.975105649 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.236842106' to each side of the equation. -1.236842106 + 1.236842106 + x = 0.975105649 + 1.236842106 Combine like terms: -1.236842106 + 1.236842106 = 0.000000000 0.000000000 + x = 0.975105649 + 1.236842106 x = 0.975105649 + 1.236842106 Combine like terms: 0.975105649 + 1.236842106 = 2.211947755 x = 2.211947755 Simplifying x = 2.211947755Subproblem 2
x + -1.236842106 = -0.975105649 Simplifying x + -1.236842106 = -0.975105649 Reorder the terms: -1.236842106 + x = -0.975105649 Solving -1.236842106 + x = -0.975105649 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.236842106' to each side of the equation. -1.236842106 + 1.236842106 + x = -0.975105649 + 1.236842106 Combine like terms: -1.236842106 + 1.236842106 = 0.000000000 0.000000000 + x = -0.975105649 + 1.236842106 x = -0.975105649 + 1.236842106 Combine like terms: -0.975105649 + 1.236842106 = 0.261736457 x = 0.261736457 Simplifying x = 0.261736457Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.211947755, 0.261736457}
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