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Simplifying (181.52 + -1x)(229.9 + -1x) = 3000 Multiply (181.52 + -1x) * (229.9 + -1x) (181.52(229.9 + -1x) + -1x * (229.9 + -1x)) = 3000 ((229.9 * 181.52 + -1x * 181.52) + -1x * (229.9 + -1x)) = 3000 ((41731.448 + -181.52x) + -1x * (229.9 + -1x)) = 3000 (41731.448 + -181.52x + (229.9 * -1x + -1x * -1x)) = 3000 (41731.448 + -181.52x + (-229.9x + 1x2)) = 3000 Combine like terms: -181.52x + -229.9x = -411.42x (41731.448 + -411.42x + 1x2) = 3000 Solving 41731.448 + -411.42x + 1x2 = 3000 Solving for variable 'x'. Reorder the terms: 41731.448 + -3000 + -411.42x + 1x2 = 3000 + -3000 Combine like terms: 41731.448 + -3000 = 38731.448 38731.448 + -411.42x + 1x2 = 3000 + -3000 Combine like terms: 3000 + -3000 = 0 38731.448 + -411.42x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '-38731.448' to each side of the equation. 38731.448 + -411.42x + -38731.448 + x2 = 0 + -38731.448 Reorder the terms: 38731.448 + -38731.448 + -411.42x + x2 = 0 + -38731.448 Combine like terms: 38731.448 + -38731.448 = 0.000 0.000 + -411.42x + x2 = 0 + -38731.448 -411.42x + x2 = 0 + -38731.448 Combine like terms: 0 + -38731.448 = -38731.448 -411.42x + x2 = -38731.448 The x term is -411.42x. Take half its coefficient (-205.71). Square it (42316.6041) and add it to both sides. Add '42316.6041' to each side of the equation. -411.42x + 42316.6041 + x2 = -38731.448 + 42316.6041 Reorder the terms: 42316.6041 + -411.42x + x2 = -38731.448 + 42316.6041 Combine like terms: -38731.448 + 42316.6041 = 3585.1561 42316.6041 + -411.42x + x2 = 3585.1561 Factor a perfect square on the left side: (x + -205.71)(x + -205.71) = 3585.1561 Calculate the square root of the right side: 59.876173057 Break this problem into two subproblems by setting (x + -205.71) equal to 59.876173057 and -59.876173057.Subproblem 1
x + -205.71 = 59.876173057 Simplifying x + -205.71 = 59.876173057 Reorder the terms: -205.71 + x = 59.876173057 Solving -205.71 + x = 59.876173057 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '205.71' to each side of the equation. -205.71 + 205.71 + x = 59.876173057 + 205.71 Combine like terms: -205.71 + 205.71 = 0.00 0.00 + x = 59.876173057 + 205.71 x = 59.876173057 + 205.71 Combine like terms: 59.876173057 + 205.71 = 265.586173057 x = 265.586173057 Simplifying x = 265.586173057Subproblem 2
x + -205.71 = -59.876173057 Simplifying x + -205.71 = -59.876173057 Reorder the terms: -205.71 + x = -59.876173057 Solving -205.71 + x = -59.876173057 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '205.71' to each side of the equation. -205.71 + 205.71 + x = -59.876173057 + 205.71 Combine like terms: -205.71 + 205.71 = 0.00 0.00 + x = -59.876173057 + 205.71 x = -59.876173057 + 205.71 Combine like terms: -59.876173057 + 205.71 = 145.833826943 x = 145.833826943 Simplifying x = 145.833826943Solution
The solution to the problem is based on the solutions from the subproblems. x = {265.586173057, 145.833826943}
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