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Simplifying x2 + -0.6667x + -2.8889 = 0 Reorder the terms: -2.8889 + -0.6667x + x2 = 0 Solving -2.8889 + -0.6667x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '2.8889' to each side of the equation. -2.8889 + -0.6667x + 2.8889 + x2 = 0 + 2.8889 Reorder the terms: -2.8889 + 2.8889 + -0.6667x + x2 = 0 + 2.8889 Combine like terms: -2.8889 + 2.8889 = 0.0000 0.0000 + -0.6667x + x2 = 0 + 2.8889 -0.6667x + x2 = 0 + 2.8889 Combine like terms: 0 + 2.8889 = 2.8889 -0.6667x + x2 = 2.8889 The x term is -0.6667x. Take half its coefficient (-0.33335). Square it (0.1111222225) and add it to both sides. Add '0.1111222225' to each side of the equation. -0.6667x + 0.1111222225 + x2 = 2.8889 + 0.1111222225 Reorder the terms: 0.1111222225 + -0.6667x + x2 = 2.8889 + 0.1111222225 Combine like terms: 2.8889 + 0.1111222225 = 3.0000222225 0.1111222225 + -0.6667x + x2 = 3.0000222225 Factor a perfect square on the left side: (x + -0.33335)(x + -0.33335) = 3.0000222225 Calculate the square root of the right side: 1.732057223 Break this problem into two subproblems by setting (x + -0.33335) equal to 1.732057223 and -1.732057223.Subproblem 1
x + -0.33335 = 1.732057223 Simplifying x + -0.33335 = 1.732057223 Reorder the terms: -0.33335 + x = 1.732057223 Solving -0.33335 + x = 1.732057223 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.33335' to each side of the equation. -0.33335 + 0.33335 + x = 1.732057223 + 0.33335 Combine like terms: -0.33335 + 0.33335 = 0.00000 0.00000 + x = 1.732057223 + 0.33335 x = 1.732057223 + 0.33335 Combine like terms: 1.732057223 + 0.33335 = 2.065407223 x = 2.065407223 Simplifying x = 2.065407223Subproblem 2
x + -0.33335 = -1.732057223 Simplifying x + -0.33335 = -1.732057223 Reorder the terms: -0.33335 + x = -1.732057223 Solving -0.33335 + x = -1.732057223 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.33335' to each side of the equation. -0.33335 + 0.33335 + x = -1.732057223 + 0.33335 Combine like terms: -0.33335 + 0.33335 = 0.00000 0.00000 + x = -1.732057223 + 0.33335 x = -1.732057223 + 0.33335 Combine like terms: -1.732057223 + 0.33335 = -1.398707223 x = -1.398707223 Simplifying x = -1.398707223Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.065407223, -1.398707223}
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