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Simplifying x2 + -73x + 320 = 0 Reorder the terms: 320 + -73x + x2 = 0 Solving 320 + -73x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-320' to each side of the equation. 320 + -73x + -320 + x2 = 0 + -320 Reorder the terms: 320 + -320 + -73x + x2 = 0 + -320 Combine like terms: 320 + -320 = 0 0 + -73x + x2 = 0 + -320 -73x + x2 = 0 + -320 Combine like terms: 0 + -320 = -320 -73x + x2 = -320 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 = -320 + 1332.25 Reorder the terms: 1332.25 + -73x + x2 = -320 + 1332.25 Combine like terms: -320 + 1332.25 = 1012.25 1332.25 + -73x + x2 = 1012.25 Factor a perfect square on the left side: (x + -36.5)(x + -36.5) = 1012.25 Calculate the square root of the right side: 31.81587654 Break this problem into two subproblems by setting (x + -36.5) equal to 31.81587654 and -31.81587654.Subproblem 1
x + -36.5 = 31.81587654 Simplifying x + -36.5 = 31.81587654 Reorder the terms: -36.5 + x = 31.81587654 Solving -36.5 + x = 31.81587654 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 = 31.81587654 + 36.5 Combine like terms: -36.5 + 36.5 = 0.0 0.0 + x = 31.81587654 + 36.5 x = 31.81587654 + 36.5 Combine like terms: 31.81587654 + 36.5 = 68.31587654 x = 68.31587654 Simplifying x = 68.31587654Subproblem 2
x + -36.5 = -31.81587654 Simplifying x + -36.5 = -31.81587654 Reorder the terms: -36.5 + x = -31.81587654 Solving -36.5 + x = -31.81587654 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 = -31.81587654 + 36.5 Combine like terms: -36.5 + 36.5 = 0.0 0.0 + x = -31.81587654 + 36.5 x = -31.81587654 + 36.5 Combine like terms: -31.81587654 + 36.5 = 4.68412346 x = 4.68412346 Simplifying x = 4.68412346Solution
The solution to the problem is based on the solutions from the subproblems. x = {68.31587654, 4.68412346}
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