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Simplifying 540.56 + -73x + -1x2 = 0 Solving 540.56 + -73x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -540.56 + 73x + x2 = 0 Move the constant term to the right: Add '540.56' to each side of the equation. -540.56 + 73x + 540.56 + x2 = 0 + 540.56 Reorder the terms: -540.56 + 540.56 + 73x + x2 = 0 + 540.56 Combine like terms: -540.56 + 540.56 = 0.00 0.00 + 73x + x2 = 0 + 540.56 73x + x2 = 0 + 540.56 Combine like terms: 0 + 540.56 = 540.56 73x + x2 = 540.56 The x term is 73x. Take half its coefficient (36.5). Square it (1332.25) and add it to both sides. Add '1332.25' to each side of the equation. 73x + 1332.25 + x2 = 540.56 + 1332.25 Reorder the terms: 1332.25 + 73x + x2 = 540.56 + 1332.25 Combine like terms: 540.56 + 1332.25 = 1872.81 1332.25 + 73x + x2 = 1872.81 Factor a perfect square on the left side: (x + 36.5)(x + 36.5) = 1872.81 Calculate the square root of the right side: 43.275974859 Break this problem into two subproblems by setting (x + 36.5) equal to 43.275974859 and -43.275974859.Subproblem 1
x + 36.5 = 43.275974859 Simplifying x + 36.5 = 43.275974859 Reorder the terms: 36.5 + x = 43.275974859 Solving 36.5 + x = 43.275974859 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-36.5' to each side of the equation. 36.5 + -36.5 + x = 43.275974859 + -36.5 Combine like terms: 36.5 + -36.5 = 0.0 0.0 + x = 43.275974859 + -36.5 x = 43.275974859 + -36.5 Combine like terms: 43.275974859 + -36.5 = 6.775974859 x = 6.775974859 Simplifying x = 6.775974859Subproblem 2
x + 36.5 = -43.275974859 Simplifying x + 36.5 = -43.275974859 Reorder the terms: 36.5 + x = -43.275974859 Solving 36.5 + x = -43.275974859 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-36.5' to each side of the equation. 36.5 + -36.5 + x = -43.275974859 + -36.5 Combine like terms: 36.5 + -36.5 = 0.0 0.0 + x = -43.275974859 + -36.5 x = -43.275974859 + -36.5 Combine like terms: -43.275974859 + -36.5 = -79.775974859 x = -79.775974859 Simplifying x = -79.775974859Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.775974859, -79.775974859}
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