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Simplifying x2 + 0.33x + -0.166 = 0 Reorder the terms: -0.166 + 0.33x + x2 = 0 Solving -0.166 + 0.33x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.166' to each side of the equation. -0.166 + 0.33x + 0.166 + x2 = 0 + 0.166 Reorder the terms: -0.166 + 0.166 + 0.33x + x2 = 0 + 0.166 Combine like terms: -0.166 + 0.166 = 0.000 0.000 + 0.33x + x2 = 0 + 0.166 0.33x + x2 = 0 + 0.166 Combine like terms: 0 + 0.166 = 0.166 0.33x + x2 = 0.166 The x term is 0.33x. Take half its coefficient (0.165). Square it (0.027225) and add it to both sides. Add '0.027225' to each side of the equation. 0.33x + 0.027225 + x2 = 0.166 + 0.027225 Reorder the terms: 0.027225 + 0.33x + x2 = 0.166 + 0.027225 Combine like terms: 0.166 + 0.027225 = 0.193225 0.027225 + 0.33x + x2 = 0.193225 Factor a perfect square on the left side: (x + 0.165)(x + 0.165) = 0.193225 Calculate the square root of the right side: 0.439573657 Break this problem into two subproblems by setting (x + 0.165) equal to 0.439573657 and -0.439573657.Subproblem 1
x + 0.165 = 0.439573657 Simplifying x + 0.165 = 0.439573657 Reorder the terms: 0.165 + x = 0.439573657 Solving 0.165 + x = 0.439573657 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.165' to each side of the equation. 0.165 + -0.165 + x = 0.439573657 + -0.165 Combine like terms: 0.165 + -0.165 = 0.000 0.000 + x = 0.439573657 + -0.165 x = 0.439573657 + -0.165 Combine like terms: 0.439573657 + -0.165 = 0.274573657 x = 0.274573657 Simplifying x = 0.274573657Subproblem 2
x + 0.165 = -0.439573657 Simplifying x + 0.165 = -0.439573657 Reorder the terms: 0.165 + x = -0.439573657 Solving 0.165 + x = -0.439573657 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.165' to each side of the equation. 0.165 + -0.165 + x = -0.439573657 + -0.165 Combine like terms: 0.165 + -0.165 = 0.000 0.000 + x = -0.439573657 + -0.165 x = -0.439573657 + -0.165 Combine like terms: -0.439573657 + -0.165 = -0.604573657 x = -0.604573657 Simplifying x = -0.604573657Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.274573657, -0.604573657}
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