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Simplifying (1 + -0.83x + 0.17x2) = 0 Remove parenthesis around (1 + -0.83x + 0.17x2) 1 + -0.83x + 0.17x2 = 0 Solving 1 + -0.83x + 0.17x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.17 the coefficient of the squared term: Divide each side by '0.17'. 5.882352941 + -4.882352941x + x2 = 0 Move the constant term to the right: Add '-5.882352941' to each side of the equation. 5.882352941 + -4.882352941x + -5.882352941 + x2 = 0 + -5.882352941 Reorder the terms: 5.882352941 + -5.882352941 + -4.882352941x + x2 = 0 + -5.882352941 Combine like terms: 5.882352941 + -5.882352941 = 0.000000000 0.000000000 + -4.882352941x + x2 = 0 + -5.882352941 -4.882352941x + x2 = 0 + -5.882352941 Combine like terms: 0 + -5.882352941 = -5.882352941 -4.882352941x + x2 = -5.882352941 The x term is -4.882352941x. Take half its coefficient (-2.441176471). Square it (5.959342563) and add it to both sides. Add '5.959342563' to each side of the equation. -4.882352941x + 5.959342563 + x2 = -5.882352941 + 5.959342563 Reorder the terms: 5.959342563 + -4.882352941x + x2 = -5.882352941 + 5.959342563 Combine like terms: -5.882352941 + 5.959342563 = 0.076989622 5.959342563 + -4.882352941x + x2 = 0.076989622 Factor a perfect square on the left side: (x + -2.441176471)(x + -2.441176471) = 0.076989622 Calculate the square root of the right side: 0.277470038 Break this problem into two subproblems by setting (x + -2.441176471) equal to 0.277470038 and -0.277470038.Subproblem 1
x + -2.441176471 = 0.277470038 Simplifying x + -2.441176471 = 0.277470038 Reorder the terms: -2.441176471 + x = 0.277470038 Solving -2.441176471 + x = 0.277470038 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.441176471' to each side of the equation. -2.441176471 + 2.441176471 + x = 0.277470038 + 2.441176471 Combine like terms: -2.441176471 + 2.441176471 = 0.000000000 0.000000000 + x = 0.277470038 + 2.441176471 x = 0.277470038 + 2.441176471 Combine like terms: 0.277470038 + 2.441176471 = 2.718646509 x = 2.718646509 Simplifying x = 2.718646509Subproblem 2
x + -2.441176471 = -0.277470038 Simplifying x + -2.441176471 = -0.277470038 Reorder the terms: -2.441176471 + x = -0.277470038 Solving -2.441176471 + x = -0.277470038 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.441176471' to each side of the equation. -2.441176471 + 2.441176471 + x = -0.277470038 + 2.441176471 Combine like terms: -2.441176471 + 2.441176471 = 0.000000000 0.000000000 + x = -0.277470038 + 2.441176471 x = -0.277470038 + 2.441176471 Combine like terms: -0.277470038 + 2.441176471 = 2.163706433 x = 2.163706433 Simplifying x = 2.163706433Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.718646509, 2.163706433}
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