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Simplifying x2 + -0.667x + -2.889 = 0 Reorder the terms: -2.889 + -0.667x + x2 = 0 Solving -2.889 + -0.667x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '2.889' to each side of the equation. -2.889 + -0.667x + 2.889 + x2 = 0 + 2.889 Reorder the terms: -2.889 + 2.889 + -0.667x + x2 = 0 + 2.889 Combine like terms: -2.889 + 2.889 = 0.000 0.000 + -0.667x + x2 = 0 + 2.889 -0.667x + x2 = 0 + 2.889 Combine like terms: 0 + 2.889 = 2.889 -0.667x + x2 = 2.889 The x term is -0.667x. Take half its coefficient (-0.3335). Square it (0.11122225) and add it to both sides. Add '0.11122225' to each side of the equation. -0.667x + 0.11122225 + x2 = 2.889 + 0.11122225 Reorder the terms: 0.11122225 + -0.667x + x2 = 2.889 + 0.11122225 Combine like terms: 2.889 + 0.11122225 = 3.00022225 0.11122225 + -0.667x + x2 = 3.00022225 Factor a perfect square on the left side: (x + -0.3335)(x + -0.3335) = 3.00022225 Calculate the square root of the right side: 1.732114964 Break this problem into two subproblems by setting (x + -0.3335) equal to 1.732114964 and -1.732114964.Subproblem 1
x + -0.3335 = 1.732114964 Simplifying x + -0.3335 = 1.732114964 Reorder the terms: -0.3335 + x = 1.732114964 Solving -0.3335 + x = 1.732114964 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3335' to each side of the equation. -0.3335 + 0.3335 + x = 1.732114964 + 0.3335 Combine like terms: -0.3335 + 0.3335 = 0.0000 0.0000 + x = 1.732114964 + 0.3335 x = 1.732114964 + 0.3335 Combine like terms: 1.732114964 + 0.3335 = 2.065614964 x = 2.065614964 Simplifying x = 2.065614964Subproblem 2
x + -0.3335 = -1.732114964 Simplifying x + -0.3335 = -1.732114964 Reorder the terms: -0.3335 + x = -1.732114964 Solving -0.3335 + x = -1.732114964 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3335' to each side of the equation. -0.3335 + 0.3335 + x = -1.732114964 + 0.3335 Combine like terms: -0.3335 + 0.3335 = 0.0000 0.0000 + x = -1.732114964 + 0.3335 x = -1.732114964 + 0.3335 Combine like terms: -1.732114964 + 0.3335 = -1.398614964 x = -1.398614964 Simplifying x = -1.398614964Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.065614964, -1.398614964}
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