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Simplifying x2 + -0.666x + -2.888 = 0 Reorder the terms: -2.888 + -0.666x + x2 = 0 Solving -2.888 + -0.666x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '2.888' to each side of the equation. -2.888 + -0.666x + 2.888 + x2 = 0 + 2.888 Reorder the terms: -2.888 + 2.888 + -0.666x + x2 = 0 + 2.888 Combine like terms: -2.888 + 2.888 = 0.000 0.000 + -0.666x + x2 = 0 + 2.888 -0.666x + x2 = 0 + 2.888 Combine like terms: 0 + 2.888 = 2.888 -0.666x + x2 = 2.888 The x term is -0.666x. Take half its coefficient (-0.333). Square it (0.110889) and add it to both sides. Add '0.110889' to each side of the equation. -0.666x + 0.110889 + x2 = 2.888 + 0.110889 Reorder the terms: 0.110889 + -0.666x + x2 = 2.888 + 0.110889 Combine like terms: 2.888 + 0.110889 = 2.998889 0.110889 + -0.666x + x2 = 2.998889 Factor a perfect square on the left side: (x + -0.333)(x + -0.333) = 2.998889 Calculate the square root of the right side: 1.73173006 Break this problem into two subproblems by setting (x + -0.333) equal to 1.73173006 and -1.73173006.Subproblem 1
x + -0.333 = 1.73173006 Simplifying x + -0.333 = 1.73173006 Reorder the terms: -0.333 + x = 1.73173006 Solving -0.333 + x = 1.73173006 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.333' to each side of the equation. -0.333 + 0.333 + x = 1.73173006 + 0.333 Combine like terms: -0.333 + 0.333 = 0.000 0.000 + x = 1.73173006 + 0.333 x = 1.73173006 + 0.333 Combine like terms: 1.73173006 + 0.333 = 2.06473006 x = 2.06473006 Simplifying x = 2.06473006Subproblem 2
x + -0.333 = -1.73173006 Simplifying x + -0.333 = -1.73173006 Reorder the terms: -0.333 + x = -1.73173006 Solving -0.333 + x = -1.73173006 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.333' to each side of the equation. -0.333 + 0.333 + x = -1.73173006 + 0.333 Combine like terms: -0.333 + 0.333 = 0.000 0.000 + x = -1.73173006 + 0.333 x = -1.73173006 + 0.333 Combine like terms: -1.73173006 + 0.333 = -1.39873006 x = -1.39873006 Simplifying x = -1.39873006Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.06473006, -1.39873006}
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