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Simplifying 2162.25 + -73x + -1x2 = 0 Solving 2162.25 + -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'. -2162.25 + 73x + x2 = 0 Move the constant term to the right: Add '2162.25' to each side of the equation. -2162.25 + 73x + 2162.25 + x2 = 0 + 2162.25 Reorder the terms: -2162.25 + 2162.25 + 73x + x2 = 0 + 2162.25 Combine like terms: -2162.25 + 2162.25 = 0.00 0.00 + 73x + x2 = 0 + 2162.25 73x + x2 = 0 + 2162.25 Combine like terms: 0 + 2162.25 = 2162.25 73x + x2 = 2162.25 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 = 2162.25 + 1332.25 Reorder the terms: 1332.25 + 73x + x2 = 2162.25 + 1332.25 Combine like terms: 2162.25 + 1332.25 = 3494.5 1332.25 + 73x + x2 = 3494.5 Factor a perfect square on the left side: (x + 36.5)(x + 36.5) = 3494.5 Calculate the square root of the right side: 59.114296071 Break this problem into two subproblems by setting (x + 36.5) equal to 59.114296071 and -59.114296071.Subproblem 1
x + 36.5 = 59.114296071 Simplifying x + 36.5 = 59.114296071 Reorder the terms: 36.5 + x = 59.114296071 Solving 36.5 + x = 59.114296071 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 = 59.114296071 + -36.5 Combine like terms: 36.5 + -36.5 = 0.0 0.0 + x = 59.114296071 + -36.5 x = 59.114296071 + -36.5 Combine like terms: 59.114296071 + -36.5 = 22.614296071 x = 22.614296071 Simplifying x = 22.614296071Subproblem 2
x + 36.5 = -59.114296071 Simplifying x + 36.5 = -59.114296071 Reorder the terms: 36.5 + x = -59.114296071 Solving 36.5 + x = -59.114296071 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 = -59.114296071 + -36.5 Combine like terms: 36.5 + -36.5 = 0.0 0.0 + x = -59.114296071 + -36.5 x = -59.114296071 + -36.5 Combine like terms: -59.114296071 + -36.5 = -95.614296071 x = -95.614296071 Simplifying x = -95.614296071Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.614296071, -95.614296071}
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