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Simplifying x2 + -321.5x = -8885 Reorder the terms: -321.5x + x2 = -8885 Solving -321.5x + x2 = -8885 Solving for variable 'x'. Reorder the terms: 8885 + -321.5x + x2 = -8885 + 8885 Combine like terms: -8885 + 8885 = 0 8885 + -321.5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-8885' to each side of the equation. 8885 + -321.5x + -8885 + x2 = 0 + -8885 Reorder the terms: 8885 + -8885 + -321.5x + x2 = 0 + -8885 Combine like terms: 8885 + -8885 = 0 0 + -321.5x + x2 = 0 + -8885 -321.5x + x2 = 0 + -8885 Combine like terms: 0 + -8885 = -8885 -321.5x + x2 = -8885 The x term is -321.5x. Take half its coefficient (-160.75). Square it (25840.5625) and add it to both sides. Add '25840.5625' to each side of the equation. -321.5x + 25840.5625 + x2 = -8885 + 25840.5625 Reorder the terms: 25840.5625 + -321.5x + x2 = -8885 + 25840.5625 Combine like terms: -8885 + 25840.5625 = 16955.5625 25840.5625 + -321.5x + x2 = 16955.5625 Factor a perfect square on the left side: (x + -160.75)(x + -160.75) = 16955.5625 Calculate the square root of the right side: 130.213526563 Break this problem into two subproblems by setting (x + -160.75) equal to 130.213526563 and -130.213526563.Subproblem 1
x + -160.75 = 130.213526563 Simplifying x + -160.75 = 130.213526563 Reorder the terms: -160.75 + x = 130.213526563 Solving -160.75 + x = 130.213526563 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '160.75' to each side of the equation. -160.75 + 160.75 + x = 130.213526563 + 160.75 Combine like terms: -160.75 + 160.75 = 0.00 0.00 + x = 130.213526563 + 160.75 x = 130.213526563 + 160.75 Combine like terms: 130.213526563 + 160.75 = 290.963526563 x = 290.963526563 Simplifying x = 290.963526563Subproblem 2
x + -160.75 = -130.213526563 Simplifying x + -160.75 = -130.213526563 Reorder the terms: -160.75 + x = -130.213526563 Solving -160.75 + x = -130.213526563 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '160.75' to each side of the equation. -160.75 + 160.75 + x = -130.213526563 + 160.75 Combine like terms: -160.75 + 160.75 = 0.00 0.00 + x = -130.213526563 + 160.75 x = -130.213526563 + 160.75 Combine like terms: -130.213526563 + 160.75 = 30.536473437 x = 30.536473437 Simplifying x = 30.536473437Solution
The solution to the problem is based on the solutions from the subproblems. x = {290.963526563, 30.536473437}
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