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Simplifying (0.0547x + 0.4058) * x + (4.2443x + 25.076) = 0 Reorder the terms: (0.4058 + 0.0547x) * x + (4.2443x + 25.076) = 0 Reorder the terms for easier multiplication: x(0.4058 + 0.0547x) + (4.2443x + 25.076) = 0 (0.4058 * x + 0.0547x * x) + (4.2443x + 25.076) = 0 (0.4058x + 0.0547x2) + (4.2443x + 25.076) = 0 Reorder the terms: 0.4058x + 0.0547x2 + (25.076 + 4.2443x) = 0 Remove parenthesis around (25.076 + 4.2443x) 0.4058x + 0.0547x2 + 25.076 + 4.2443x = 0 Reorder the terms: 25.076 + 0.4058x + 4.2443x + 0.0547x2 = 0 Combine like terms: 0.4058x + 4.2443x = 4.6501x 25.076 + 4.6501x + 0.0547x2 = 0 Solving 25.076 + 4.6501x + 0.0547x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.0547 the coefficient of the squared term: Divide each side by '0.0547'. 458.4277879 + 85.01096892x + x2 = 0 Move the constant term to the right: Add '-458.4277879' to each side of the equation. 458.4277879 + 85.01096892x + -458.4277879 + x2 = 0 + -458.4277879 Reorder the terms: 458.4277879 + -458.4277879 + 85.01096892x + x2 = 0 + -458.4277879 Combine like terms: 458.4277879 + -458.4277879 = 0.0000000 0.0000000 + 85.01096892x + x2 = 0 + -458.4277879 85.01096892x + x2 = 0 + -458.4277879 Combine like terms: 0 + -458.4277879 = -458.4277879 85.01096892x + x2 = -458.4277879 The x term is 85.01096892x. Take half its coefficient (42.50548446). Square it (1806.716209) and add it to both sides. Add '1806.716209' to each side of the equation. 85.01096892x + 1806.716209 + x2 = -458.4277879 + 1806.716209 Reorder the terms: 1806.716209 + 85.01096892x + x2 = -458.4277879 + 1806.716209 Combine like terms: -458.4277879 + 1806.716209 = 1348.2884211 1806.716209 + 85.01096892x + x2 = 1348.2884211 Factor a perfect square on the left side: (x + 42.50548446)(x + 42.50548446) = 1348.2884211 Calculate the square root of the right side: 36.719047116 Break this problem into two subproblems by setting (x + 42.50548446) equal to 36.719047116 and -36.719047116.Subproblem 1
x + 42.50548446 = 36.719047116 Simplifying x + 42.50548446 = 36.719047116 Reorder the terms: 42.50548446 + x = 36.719047116 Solving 42.50548446 + x = 36.719047116 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-42.50548446' to each side of the equation. 42.50548446 + -42.50548446 + x = 36.719047116 + -42.50548446 Combine like terms: 42.50548446 + -42.50548446 = 0.00000000 0.00000000 + x = 36.719047116 + -42.50548446 x = 36.719047116 + -42.50548446 Combine like terms: 36.719047116 + -42.50548446 = -5.786437344 x = -5.786437344 Simplifying x = -5.786437344Subproblem 2
x + 42.50548446 = -36.719047116 Simplifying x + 42.50548446 = -36.719047116 Reorder the terms: 42.50548446 + x = -36.719047116 Solving 42.50548446 + x = -36.719047116 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-42.50548446' to each side of the equation. 42.50548446 + -42.50548446 + x = -36.719047116 + -42.50548446 Combine like terms: 42.50548446 + -42.50548446 = 0.00000000 0.00000000 + x = -36.719047116 + -42.50548446 x = -36.719047116 + -42.50548446 Combine like terms: -36.719047116 + -42.50548446 = -79.224531576 x = -79.224531576 Simplifying x = -79.224531576Solution
The solution to the problem is based on the solutions from the subproblems. x = {-5.786437344, -79.224531576}
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