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Simplifying x2 + -73x + 1040 = 0 Reorder the terms: 1040 + -73x + x2 = 0 Solving 1040 + -73x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-1040' to each side of the equation. 1040 + -73x + -1040 + x2 = 0 + -1040 Reorder the terms: 1040 + -1040 + -73x + x2 = 0 + -1040 Combine like terms: 1040 + -1040 = 0 0 + -73x + x2 = 0 + -1040 -73x + x2 = 0 + -1040 Combine like terms: 0 + -1040 = -1040 -73x + x2 = -1040 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 = -1040 + 1332.25 Reorder the terms: 1332.25 + -73x + x2 = -1040 + 1332.25 Combine like terms: -1040 + 1332.25 = 292.25 1332.25 + -73x + x2 = 292.25 Factor a perfect square on the left side: (x + -36.5)(x + -36.5) = 292.25 Calculate the square root of the right side: 17.095320997 Break this problem into two subproblems by setting (x + -36.5) equal to 17.095320997 and -17.095320997.Subproblem 1
x + -36.5 = 17.095320997 Simplifying x + -36.5 = 17.095320997 Reorder the terms: -36.5 + x = 17.095320997 Solving -36.5 + x = 17.095320997 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 = 17.095320997 + 36.5 Combine like terms: -36.5 + 36.5 = 0.0 0.0 + x = 17.095320997 + 36.5 x = 17.095320997 + 36.5 Combine like terms: 17.095320997 + 36.5 = 53.595320997 x = 53.595320997 Simplifying x = 53.595320997Subproblem 2
x + -36.5 = -17.095320997 Simplifying x + -36.5 = -17.095320997 Reorder the terms: -36.5 + x = -17.095320997 Solving -36.5 + x = -17.095320997 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 = -17.095320997 + 36.5 Combine like terms: -36.5 + 36.5 = 0.0 0.0 + x = -17.095320997 + 36.5 x = -17.095320997 + 36.5 Combine like terms: -17.095320997 + 36.5 = 19.404679003 x = 19.404679003 Simplifying x = 19.404679003Solution
The solution to the problem is based on the solutions from the subproblems. x = {53.595320997, 19.404679003}
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