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Simplifying 6.28x2 + 540.08x + -4173 = 0 Reorder the terms: -4173 + 540.08x + 6.28x2 = 0 Solving -4173 + 540.08x + 6.28x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6.28 the coefficient of the squared term: Divide each side by '6.28'. -664.4904459 + 86x + x2 = 0 Move the constant term to the right: Add '664.4904459' to each side of the equation. -664.4904459 + 86x + 664.4904459 + x2 = 0 + 664.4904459 Reorder the terms: -664.4904459 + 664.4904459 + 86x + x2 = 0 + 664.4904459 Combine like terms: -664.4904459 + 664.4904459 = 0.0000000 0.0000000 + 86x + x2 = 0 + 664.4904459 86x + x2 = 0 + 664.4904459 Combine like terms: 0 + 664.4904459 = 664.4904459 86x + x2 = 664.4904459 The x term is 86x. Take half its coefficient (43). Square it (1849) and add it to both sides. Add '1849' to each side of the equation. 86x + 1849 + x2 = 664.4904459 + 1849 Reorder the terms: 1849 + 86x + x2 = 664.4904459 + 1849 Combine like terms: 664.4904459 + 1849 = 2513.4904459 1849 + 86x + x2 = 2513.4904459 Factor a perfect square on the left side: (x + 43)(x + 43) = 2513.4904459 Calculate the square root of the right side: 50.134722956 Break this problem into two subproblems by setting (x + 43) equal to 50.134722956 and -50.134722956.Subproblem 1
x + 43 = 50.134722956 Simplifying x + 43 = 50.134722956 Reorder the terms: 43 + x = 50.134722956 Solving 43 + x = 50.134722956 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-43' to each side of the equation. 43 + -43 + x = 50.134722956 + -43 Combine like terms: 43 + -43 = 0 0 + x = 50.134722956 + -43 x = 50.134722956 + -43 Combine like terms: 50.134722956 + -43 = 7.134722956 x = 7.134722956 Simplifying x = 7.134722956Subproblem 2
x + 43 = -50.134722956 Simplifying x + 43 = -50.134722956 Reorder the terms: 43 + x = -50.134722956 Solving 43 + x = -50.134722956 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-43' to each side of the equation. 43 + -43 + x = -50.134722956 + -43 Combine like terms: 43 + -43 = 0 0 + x = -50.134722956 + -43 x = -50.134722956 + -43 Combine like terms: -50.134722956 + -43 = -93.134722956 x = -93.134722956 Simplifying x = -93.134722956Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.134722956, -93.134722956}
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