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Simplifying x2 + -150x + 3500 = 0 Reorder the terms: 3500 + -150x + x2 = 0 Solving 3500 + -150x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-3500' to each side of the equation. 3500 + -150x + -3500 + x2 = 0 + -3500 Reorder the terms: 3500 + -3500 + -150x + x2 = 0 + -3500 Combine like terms: 3500 + -3500 = 0 0 + -150x + x2 = 0 + -3500 -150x + x2 = 0 + -3500 Combine like terms: 0 + -3500 = -3500 -150x + x2 = -3500 The x term is -150x. Take half its coefficient (-75). Square it (5625) and add it to both sides. Add '5625' to each side of the equation. -150x + 5625 + x2 = -3500 + 5625 Reorder the terms: 5625 + -150x + x2 = -3500 + 5625 Combine like terms: -3500 + 5625 = 2125 5625 + -150x + x2 = 2125 Factor a perfect square on the left side: (x + -75)(x + -75) = 2125 Calculate the square root of the right side: 46.097722286 Break this problem into two subproblems by setting (x + -75) equal to 46.097722286 and -46.097722286.Subproblem 1
x + -75 = 46.097722286 Simplifying x + -75 = 46.097722286 Reorder the terms: -75 + x = 46.097722286 Solving -75 + x = 46.097722286 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '75' to each side of the equation. -75 + 75 + x = 46.097722286 + 75 Combine like terms: -75 + 75 = 0 0 + x = 46.097722286 + 75 x = 46.097722286 + 75 Combine like terms: 46.097722286 + 75 = 121.097722286 x = 121.097722286 Simplifying x = 121.097722286Subproblem 2
x + -75 = -46.097722286 Simplifying x + -75 = -46.097722286 Reorder the terms: -75 + x = -46.097722286 Solving -75 + x = -46.097722286 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '75' to each side of the equation. -75 + 75 + x = -46.097722286 + 75 Combine like terms: -75 + 75 = 0 0 + x = -46.097722286 + 75 x = -46.097722286 + 75 Combine like terms: -46.097722286 + 75 = 28.902277714 x = 28.902277714 Simplifying x = 28.902277714Solution
The solution to the problem is based on the solutions from the subproblems. x = {121.097722286, 28.902277714}
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