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Simplifying -6x + x2 + 44.8 * 0.001 = 0 Multiply 44.8 * 0.001 -6x + x2 + 0.0448 = 0 Reorder the terms: 0.0448 + -6x + x2 = 0 Solving 0.0448 + -6x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.0448' to each side of the equation. 0.0448 + -6x + -0.0448 + x2 = 0 + -0.0448 Reorder the terms: 0.0448 + -0.0448 + -6x + x2 = 0 + -0.0448 Combine like terms: 0.0448 + -0.0448 = 0.0000 0.0000 + -6x + x2 = 0 + -0.0448 -6x + x2 = 0 + -0.0448 Combine like terms: 0 + -0.0448 = -0.0448 -6x + x2 = -0.0448 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = -0.0448 + 9 Reorder the terms: 9 + -6x + x2 = -0.0448 + 9 Combine like terms: -0.0448 + 9 = 8.9552 9 + -6x + x2 = 8.9552 Factor a perfect square on the left side: (x + -3)(x + -3) = 8.9552 Calculate the square root of the right side: 2.992524018 Break this problem into two subproblems by setting (x + -3) equal to 2.992524018 and -2.992524018.Subproblem 1
x + -3 = 2.992524018 Simplifying x + -3 = 2.992524018 Reorder the terms: -3 + x = 2.992524018 Solving -3 + x = 2.992524018 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 2.992524018 + 3 Combine like terms: -3 + 3 = 0 0 + x = 2.992524018 + 3 x = 2.992524018 + 3 Combine like terms: 2.992524018 + 3 = 5.992524018 x = 5.992524018 Simplifying x = 5.992524018Subproblem 2
x + -3 = -2.992524018 Simplifying x + -3 = -2.992524018 Reorder the terms: -3 + x = -2.992524018 Solving -3 + x = -2.992524018 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -2.992524018 + 3 Combine like terms: -3 + 3 = 0 0 + x = -2.992524018 + 3 x = -2.992524018 + 3 Combine like terms: -2.992524018 + 3 = 0.007475982 x = 0.007475982 Simplifying x = 0.007475982Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.992524018, 0.007475982}
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