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Simplifying (1 + -0.833x + 0.167x2) = 0 Remove parenthesis around (1 + -0.833x + 0.167x2) 1 + -0.833x + 0.167x2 = 0 Solving 1 + -0.833x + 0.167x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.167 the coefficient of the squared term: Divide each side by '0.167'. 5.988023952 + -4.988023952x + x2 = 0 Move the constant term to the right: Add '-5.988023952' to each side of the equation. 5.988023952 + -4.988023952x + -5.988023952 + x2 = 0 + -5.988023952 Reorder the terms: 5.988023952 + -5.988023952 + -4.988023952x + x2 = 0 + -5.988023952 Combine like terms: 5.988023952 + -5.988023952 = 0.000000000 0.000000000 + -4.988023952x + x2 = 0 + -5.988023952 -4.988023952x + x2 = 0 + -5.988023952 Combine like terms: 0 + -5.988023952 = -5.988023952 -4.988023952x + x2 = -5.988023952 The x term is -4.988023952x. Take half its coefficient (-2.494011976). Square it (6.220095736) and add it to both sides. Add '6.220095736' to each side of the equation. -4.988023952x + 6.220095736 + x2 = -5.988023952 + 6.220095736 Reorder the terms: 6.220095736 + -4.988023952x + x2 = -5.988023952 + 6.220095736 Combine like terms: -5.988023952 + 6.220095736 = 0.232071784 6.220095736 + -4.988023952x + x2 = 0.232071784 Factor a perfect square on the left side: (x + -2.494011976)(x + -2.494011976) = 0.232071784 Calculate the square root of the right side: 0.481738294 Break this problem into two subproblems by setting (x + -2.494011976) equal to 0.481738294 and -0.481738294.Subproblem 1
x + -2.494011976 = 0.481738294 Simplifying x + -2.494011976 = 0.481738294 Reorder the terms: -2.494011976 + x = 0.481738294 Solving -2.494011976 + x = 0.481738294 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.494011976' to each side of the equation. -2.494011976 + 2.494011976 + x = 0.481738294 + 2.494011976 Combine like terms: -2.494011976 + 2.494011976 = 0.000000000 0.000000000 + x = 0.481738294 + 2.494011976 x = 0.481738294 + 2.494011976 Combine like terms: 0.481738294 + 2.494011976 = 2.97575027 x = 2.97575027 Simplifying x = 2.97575027Subproblem 2
x + -2.494011976 = -0.481738294 Simplifying x + -2.494011976 = -0.481738294 Reorder the terms: -2.494011976 + x = -0.481738294 Solving -2.494011976 + x = -0.481738294 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.494011976' to each side of the equation. -2.494011976 + 2.494011976 + x = -0.481738294 + 2.494011976 Combine like terms: -2.494011976 + 2.494011976 = 0.000000000 0.000000000 + x = -0.481738294 + 2.494011976 x = -0.481738294 + 2.494011976 Combine like terms: -0.481738294 + 2.494011976 = 2.012273682 x = 2.012273682 Simplifying x = 2.012273682Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.97575027, 2.012273682}
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