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Simplifying 2.06x2 + 77.85x + -490.96 = 0 Reorder the terms: -490.96 + 77.85x + 2.06x2 = 0 Solving -490.96 + 77.85x + 2.06x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2.06 the coefficient of the squared term: Divide each side by '2.06'. -238.3300971 + 37.79126214x + x2 = 0 Move the constant term to the right: Add '238.3300971' to each side of the equation. -238.3300971 + 37.79126214x + 238.3300971 + x2 = 0 + 238.3300971 Reorder the terms: -238.3300971 + 238.3300971 + 37.79126214x + x2 = 0 + 238.3300971 Combine like terms: -238.3300971 + 238.3300971 = 0.0000000 0.0000000 + 37.79126214x + x2 = 0 + 238.3300971 37.79126214x + x2 = 0 + 238.3300971 Combine like terms: 0 + 238.3300971 = 238.3300971 37.79126214x + x2 = 238.3300971 The x term is 37.79126214x. Take half its coefficient (18.89563107). Square it (357.0448735) and add it to both sides. Add '357.0448735' to each side of the equation. 37.79126214x + 357.0448735 + x2 = 238.3300971 + 357.0448735 Reorder the terms: 357.0448735 + 37.79126214x + x2 = 238.3300971 + 357.0448735 Combine like terms: 238.3300971 + 357.0448735 = 595.3749706 357.0448735 + 37.79126214x + x2 = 595.3749706 Factor a perfect square on the left side: (x + 18.89563107)(x + 18.89563107) = 595.3749706 Calculate the square root of the right side: 24.400306773 Break this problem into two subproblems by setting (x + 18.89563107) equal to 24.400306773 and -24.400306773.Subproblem 1
x + 18.89563107 = 24.400306773 Simplifying x + 18.89563107 = 24.400306773 Reorder the terms: 18.89563107 + x = 24.400306773 Solving 18.89563107 + x = 24.400306773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18.89563107' to each side of the equation. 18.89563107 + -18.89563107 + x = 24.400306773 + -18.89563107 Combine like terms: 18.89563107 + -18.89563107 = 0.00000000 0.00000000 + x = 24.400306773 + -18.89563107 x = 24.400306773 + -18.89563107 Combine like terms: 24.400306773 + -18.89563107 = 5.504675703 x = 5.504675703 Simplifying x = 5.504675703Subproblem 2
x + 18.89563107 = -24.400306773 Simplifying x + 18.89563107 = -24.400306773 Reorder the terms: 18.89563107 + x = -24.400306773 Solving 18.89563107 + x = -24.400306773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18.89563107' to each side of the equation. 18.89563107 + -18.89563107 + x = -24.400306773 + -18.89563107 Combine like terms: 18.89563107 + -18.89563107 = 0.00000000 0.00000000 + x = -24.400306773 + -18.89563107 x = -24.400306773 + -18.89563107 Combine like terms: -24.400306773 + -18.89563107 = -43.295937843 x = -43.295937843 Simplifying x = -43.295937843Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.504675703, -43.295937843}
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