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Simplifying x2 + -0.666x + -3.222 = 0 Reorder the terms: -3.222 + -0.666x + x2 = 0 Solving -3.222 + -0.666x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '3.222' to each side of the equation. -3.222 + -0.666x + 3.222 + x2 = 0 + 3.222 Reorder the terms: -3.222 + 3.222 + -0.666x + x2 = 0 + 3.222 Combine like terms: -3.222 + 3.222 = 0.000 0.000 + -0.666x + x2 = 0 + 3.222 -0.666x + x2 = 0 + 3.222 Combine like terms: 0 + 3.222 = 3.222 -0.666x + x2 = 3.222 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 = 3.222 + 0.110889 Reorder the terms: 0.110889 + -0.666x + x2 = 3.222 + 0.110889 Combine like terms: 3.222 + 0.110889 = 3.332889 0.110889 + -0.666x + x2 = 3.332889 Factor a perfect square on the left side: (x + -0.333)(x + -0.333) = 3.332889 Calculate the square root of the right side: 1.825620169 Break this problem into two subproblems by setting (x + -0.333) equal to 1.825620169 and -1.825620169.Subproblem 1
x + -0.333 = 1.825620169 Simplifying x + -0.333 = 1.825620169 Reorder the terms: -0.333 + x = 1.825620169 Solving -0.333 + x = 1.825620169 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 = 1.825620169 + 0.333 Combine like terms: -0.333 + 0.333 = 0.000 0.000 + x = 1.825620169 + 0.333 x = 1.825620169 + 0.333 Combine like terms: 1.825620169 + 0.333 = 2.158620169 x = 2.158620169 Simplifying x = 2.158620169Subproblem 2
x + -0.333 = -1.825620169 Simplifying x + -0.333 = -1.825620169 Reorder the terms: -0.333 + x = -1.825620169 Solving -0.333 + x = -1.825620169 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 = -1.825620169 + 0.333 Combine like terms: -0.333 + 0.333 = 0.000 0.000 + x = -1.825620169 + 0.333 x = -1.825620169 + 0.333 Combine like terms: -1.825620169 + 0.333 = -1.492620169 x = -1.492620169 Simplifying x = -1.492620169Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.158620169, -1.492620169}
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