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Simplifying x2 + -300x + 3500 = 0 Reorder the terms: 3500 + -300x + x2 = 0 Solving 3500 + -300x + 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 + -300x + -3500 + x2 = 0 + -3500 Reorder the terms: 3500 + -3500 + -300x + x2 = 0 + -3500 Combine like terms: 3500 + -3500 = 0 0 + -300x + x2 = 0 + -3500 -300x + x2 = 0 + -3500 Combine like terms: 0 + -3500 = -3500 -300x + x2 = -3500 The x term is -300x. Take half its coefficient (-150). Square it (22500) and add it to both sides. Add '22500' to each side of the equation. -300x + 22500 + x2 = -3500 + 22500 Reorder the terms: 22500 + -300x + x2 = -3500 + 22500 Combine like terms: -3500 + 22500 = 19000 22500 + -300x + x2 = 19000 Factor a perfect square on the left side: (x + -150)(x + -150) = 19000 Calculate the square root of the right side: 137.840487521 Break this problem into two subproblems by setting (x + -150) equal to 137.840487521 and -137.840487521.Subproblem 1
x + -150 = 137.840487521 Simplifying x + -150 = 137.840487521 Reorder the terms: -150 + x = 137.840487521 Solving -150 + x = 137.840487521 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '150' to each side of the equation. -150 + 150 + x = 137.840487521 + 150 Combine like terms: -150 + 150 = 0 0 + x = 137.840487521 + 150 x = 137.840487521 + 150 Combine like terms: 137.840487521 + 150 = 287.840487521 x = 287.840487521 Simplifying x = 287.840487521Subproblem 2
x + -150 = -137.840487521 Simplifying x + -150 = -137.840487521 Reorder the terms: -150 + x = -137.840487521 Solving -150 + x = -137.840487521 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '150' to each side of the equation. -150 + 150 + x = -137.840487521 + 150 Combine like terms: -150 + 150 = 0 0 + x = -137.840487521 + 150 x = -137.840487521 + 150 Combine like terms: -137.840487521 + 150 = 12.159512479 x = 12.159512479 Simplifying x = 12.159512479Solution
The solution to the problem is based on the solutions from the subproblems. x = {287.840487521, 12.159512479}
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