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Simplifying 11x2 + -28x + 1 = 0 Reorder the terms: 1 + -28x + 11x2 = 0 Solving 1 + -28x + 11x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. 0.09090909091 + -2.545454545x + x2 = 0 Move the constant term to the right: Add '-0.09090909091' to each side of the equation. 0.09090909091 + -2.545454545x + -0.09090909091 + x2 = 0 + -0.09090909091 Reorder the terms: 0.09090909091 + -0.09090909091 + -2.545454545x + x2 = 0 + -0.09090909091 Combine like terms: 0.09090909091 + -0.09090909091 = 0.00000000000 0.00000000000 + -2.545454545x + x2 = 0 + -0.09090909091 -2.545454545x + x2 = 0 + -0.09090909091 Combine like terms: 0 + -0.09090909091 = -0.09090909091 -2.545454545x + x2 = -0.09090909091 The x term is -2.545454545x. Take half its coefficient (-1.272727273). Square it (1.619834711) and add it to both sides. Add '1.619834711' to each side of the equation. -2.545454545x + 1.619834711 + x2 = -0.09090909091 + 1.619834711 Reorder the terms: 1.619834711 + -2.545454545x + x2 = -0.09090909091 + 1.619834711 Combine like terms: -0.09090909091 + 1.619834711 = 1.52892562009 1.619834711 + -2.545454545x + x2 = 1.52892562009 Factor a perfect square on the left side: (x + -1.272727273)(x + -1.272727273) = 1.52892562009 Calculate the square root of the right side: 1.236497319 Break this problem into two subproblems by setting (x + -1.272727273) equal to 1.236497319 and -1.236497319.Subproblem 1
x + -1.272727273 = 1.236497319 Simplifying x + -1.272727273 = 1.236497319 Reorder the terms: -1.272727273 + x = 1.236497319 Solving -1.272727273 + x = 1.236497319 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.272727273' to each side of the equation. -1.272727273 + 1.272727273 + x = 1.236497319 + 1.272727273 Combine like terms: -1.272727273 + 1.272727273 = 0.000000000 0.000000000 + x = 1.236497319 + 1.272727273 x = 1.236497319 + 1.272727273 Combine like terms: 1.236497319 + 1.272727273 = 2.509224592 x = 2.509224592 Simplifying x = 2.509224592Subproblem 2
x + -1.272727273 = -1.236497319 Simplifying x + -1.272727273 = -1.236497319 Reorder the terms: -1.272727273 + x = -1.236497319 Solving -1.272727273 + x = -1.236497319 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.272727273' to each side of the equation. -1.272727273 + 1.272727273 + x = -1.236497319 + 1.272727273 Combine like terms: -1.272727273 + 1.272727273 = 0.000000000 0.000000000 + x = -1.236497319 + 1.272727273 x = -1.236497319 + 1.272727273 Combine like terms: -1.236497319 + 1.272727273 = 0.036229954 x = 0.036229954 Simplifying x = 0.036229954Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.509224592, 0.036229954}
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