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Simplifying 0.167x2 + -0.333x + -1 = 0 Reorder the terms: -1 + -0.333x + 0.167x2 = 0 Solving -1 + -0.333x + 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 + -1.994011976x + x2 = 0 Move the constant term to the right: Add '5.988023952' to each side of the equation. -5.988023952 + -1.994011976x + 5.988023952 + x2 = 0 + 5.988023952 Reorder the terms: -5.988023952 + 5.988023952 + -1.994011976x + x2 = 0 + 5.988023952 Combine like terms: -5.988023952 + 5.988023952 = 0.000000000 0.000000000 + -1.994011976x + x2 = 0 + 5.988023952 -1.994011976x + x2 = 0 + 5.988023952 Combine like terms: 0 + 5.988023952 = 5.988023952 -1.994011976x + x2 = 5.988023952 The x term is -1.994011976x. Take half its coefficient (-0.997005988). Square it (0.9940209401) and add it to both sides. Add '0.9940209401' to each side of the equation. -1.994011976x + 0.9940209401 + x2 = 5.988023952 + 0.9940209401 Reorder the terms: 0.9940209401 + -1.994011976x + x2 = 5.988023952 + 0.9940209401 Combine like terms: 5.988023952 + 0.9940209401 = 6.9820448921 0.9940209401 + -1.994011976x + x2 = 6.9820448921 Factor a perfect square on the left side: (x + -0.997005988)(x + -0.997005988) = 6.9820448921 Calculate the square root of the right side: 2.642355936 Break this problem into two subproblems by setting (x + -0.997005988) equal to 2.642355936 and -2.642355936.Subproblem 1
x + -0.997005988 = 2.642355936 Simplifying x + -0.997005988 = 2.642355936 Reorder the terms: -0.997005988 + x = 2.642355936 Solving -0.997005988 + x = 2.642355936 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.997005988' to each side of the equation. -0.997005988 + 0.997005988 + x = 2.642355936 + 0.997005988 Combine like terms: -0.997005988 + 0.997005988 = 0.000000000 0.000000000 + x = 2.642355936 + 0.997005988 x = 2.642355936 + 0.997005988 Combine like terms: 2.642355936 + 0.997005988 = 3.639361924 x = 3.639361924 Simplifying x = 3.639361924Subproblem 2
x + -0.997005988 = -2.642355936 Simplifying x + -0.997005988 = -2.642355936 Reorder the terms: -0.997005988 + x = -2.642355936 Solving -0.997005988 + x = -2.642355936 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.997005988' to each side of the equation. -0.997005988 + 0.997005988 + x = -2.642355936 + 0.997005988 Combine like terms: -0.997005988 + 0.997005988 = 0.000000000 0.000000000 + x = -2.642355936 + 0.997005988 x = -2.642355936 + 0.997005988 Combine like terms: -2.642355936 + 0.997005988 = -1.645349948 x = -1.645349948 Simplifying x = -1.645349948Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.639361924, -1.645349948}
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