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Simplifying 0.3333x2 + 0.16666x + -1 = 0 Reorder the terms: -1 + 0.16666x + 0.3333x2 = 0 Solving -1 + 0.16666x + 0.3333x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.3333 the coefficient of the squared term: Divide each side by '0.3333'. -3.00030003 + 0.500030003x + x2 = 0 Move the constant term to the right: Add '3.00030003' to each side of the equation. -3.00030003 + 0.500030003x + 3.00030003 + x2 = 0 + 3.00030003 Reorder the terms: -3.00030003 + 3.00030003 + 0.500030003x + x2 = 0 + 3.00030003 Combine like terms: -3.00030003 + 3.00030003 = 0.00000000 0.00000000 + 0.500030003x + x2 = 0 + 3.00030003 0.500030003x + x2 = 0 + 3.00030003 Combine like terms: 0 + 3.00030003 = 3.00030003 0.500030003x + x2 = 3.00030003 The x term is 0.500030003x. Take half its coefficient (0.2500150015). Square it (0.06250750098) and add it to both sides. Add '0.06250750098' to each side of the equation. 0.500030003x + 0.06250750098 + x2 = 3.00030003 + 0.06250750098 Reorder the terms: 0.06250750098 + 0.500030003x + x2 = 3.00030003 + 0.06250750098 Combine like terms: 3.00030003 + 0.06250750098 = 3.06280753098 0.06250750098 + 0.500030003x + x2 = 3.06280753098 Factor a perfect square on the left side: (x + 0.2500150015)(x + 0.2500150015) = 3.06280753098 Calculate the square root of the right side: 1.750087864 Break this problem into two subproblems by setting (x + 0.2500150015) equal to 1.750087864 and -1.750087864.Subproblem 1
x + 0.2500150015 = 1.750087864 Simplifying x + 0.2500150015 = 1.750087864 Reorder the terms: 0.2500150015 + x = 1.750087864 Solving 0.2500150015 + x = 1.750087864 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2500150015' to each side of the equation. 0.2500150015 + -0.2500150015 + x = 1.750087864 + -0.2500150015 Combine like terms: 0.2500150015 + -0.2500150015 = 0.0000000000 0.0000000000 + x = 1.750087864 + -0.2500150015 x = 1.750087864 + -0.2500150015 Combine like terms: 1.750087864 + -0.2500150015 = 1.5000728625 x = 1.5000728625 Simplifying x = 1.5000728625Subproblem 2
x + 0.2500150015 = -1.750087864 Simplifying x + 0.2500150015 = -1.750087864 Reorder the terms: 0.2500150015 + x = -1.750087864 Solving 0.2500150015 + x = -1.750087864 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2500150015' to each side of the equation. 0.2500150015 + -0.2500150015 + x = -1.750087864 + -0.2500150015 Combine like terms: 0.2500150015 + -0.2500150015 = 0.0000000000 0.0000000000 + x = -1.750087864 + -0.2500150015 x = -1.750087864 + -0.2500150015 Combine like terms: -1.750087864 + -0.2500150015 = -2.0001028655 x = -2.0001028655 Simplifying x = -2.0001028655Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.5000728625, -2.0001028655}
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