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Simplifying 209.74x2 + 29216.8x + -302704 = 0 Reorder the terms: -302704 + 29216.8x + 209.74x2 = 0 Solving -302704 + 29216.8x + 209.74x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 209.74 the coefficient of the squared term: Divide each side by '209.74'. -1443.234481 + 139.3000858x + x2 = 0 Move the constant term to the right: Add '1443.234481' to each side of the equation. -1443.234481 + 139.3000858x + 1443.234481 + x2 = 0 + 1443.234481 Reorder the terms: -1443.234481 + 1443.234481 + 139.3000858x + x2 = 0 + 1443.234481 Combine like terms: -1443.234481 + 1443.234481 = 0.000000 0.000000 + 139.3000858x + x2 = 0 + 1443.234481 139.3000858x + x2 = 0 + 1443.234481 Combine like terms: 0 + 1443.234481 = 1443.234481 139.3000858x + x2 = 1443.234481 The x term is 139.3000858x. Take half its coefficient (69.6500429). Square it (4851.128476) and add it to both sides. Add '4851.128476' to each side of the equation. 139.3000858x + 4851.128476 + x2 = 1443.234481 + 4851.128476 Reorder the terms: 4851.128476 + 139.3000858x + x2 = 1443.234481 + 4851.128476 Combine like terms: 1443.234481 + 4851.128476 = 6294.362957 4851.128476 + 139.3000858x + x2 = 6294.362957 Factor a perfect square on the left side: (x + 69.6500429)(x + 69.6500429) = 6294.362957 Calculate the square root of the right side: 79.337021352 Break this problem into two subproblems by setting (x + 69.6500429) equal to 79.337021352 and -79.337021352.Subproblem 1
x + 69.6500429 = 79.337021352 Simplifying x + 69.6500429 = 79.337021352 Reorder the terms: 69.6500429 + x = 79.337021352 Solving 69.6500429 + x = 79.337021352 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-69.6500429' to each side of the equation. 69.6500429 + -69.6500429 + x = 79.337021352 + -69.6500429 Combine like terms: 69.6500429 + -69.6500429 = 0.0000000 0.0000000 + x = 79.337021352 + -69.6500429 x = 79.337021352 + -69.6500429 Combine like terms: 79.337021352 + -69.6500429 = 9.686978452 x = 9.686978452 Simplifying x = 9.686978452Subproblem 2
x + 69.6500429 = -79.337021352 Simplifying x + 69.6500429 = -79.337021352 Reorder the terms: 69.6500429 + x = -79.337021352 Solving 69.6500429 + x = -79.337021352 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-69.6500429' to each side of the equation. 69.6500429 + -69.6500429 + x = -79.337021352 + -69.6500429 Combine like terms: 69.6500429 + -69.6500429 = 0.0000000 0.0000000 + x = -79.337021352 + -69.6500429 x = -79.337021352 + -69.6500429 Combine like terms: -79.337021352 + -69.6500429 = -148.987064252 x = -148.987064252 Simplifying x = -148.987064252Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.686978452, -148.987064252}
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