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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 = -0.007475982 x = -0.007475982 Simplifying x = -0.007475982Subproblem 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 = -5.992524018 x = -5.992524018 Simplifying x = -5.992524018Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.007475982, -5.992524018}
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