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Simplifying x2 + 75x + -2250 = 0 Reorder the terms: -2250 + 75x + x2 = 0 Solving -2250 + 75x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '2250' to each side of the equation. -2250 + 75x + 2250 + x2 = 0 + 2250 Reorder the terms: -2250 + 2250 + 75x + x2 = 0 + 2250 Combine like terms: -2250 + 2250 = 0 0 + 75x + x2 = 0 + 2250 75x + x2 = 0 + 2250 Combine like terms: 0 + 2250 = 2250 75x + x2 = 2250 The x term is 75x. Take half its coefficient (37.5). Square it (1406.25) and add it to both sides. Add '1406.25' to each side of the equation. 75x + 1406.25 + x2 = 2250 + 1406.25 Reorder the terms: 1406.25 + 75x + x2 = 2250 + 1406.25 Combine like terms: 2250 + 1406.25 = 3656.25 1406.25 + 75x + x2 = 3656.25 Factor a perfect square on the left side: (x + 37.5)(x + 37.5) = 3656.25 Calculate the square root of the right side: 60.466933112 Break this problem into two subproblems by setting (x + 37.5) equal to 60.466933112 and -60.466933112.Subproblem 1
x + 37.5 = 60.466933112 Simplifying x + 37.5 = 60.466933112 Reorder the terms: 37.5 + x = 60.466933112 Solving 37.5 + x = 60.466933112 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-37.5' to each side of the equation. 37.5 + -37.5 + x = 60.466933112 + -37.5 Combine like terms: 37.5 + -37.5 = 0.0 0.0 + x = 60.466933112 + -37.5 x = 60.466933112 + -37.5 Combine like terms: 60.466933112 + -37.5 = 22.966933112 x = 22.966933112 Simplifying x = 22.966933112Subproblem 2
x + 37.5 = -60.466933112 Simplifying x + 37.5 = -60.466933112 Reorder the terms: 37.5 + x = -60.466933112 Solving 37.5 + x = -60.466933112 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-37.5' to each side of the equation. 37.5 + -37.5 + x = -60.466933112 + -37.5 Combine like terms: 37.5 + -37.5 = 0.0 0.0 + x = -60.466933112 + -37.5 x = -60.466933112 + -37.5 Combine like terms: -60.466933112 + -37.5 = -97.966933112 x = -97.966933112 Simplifying x = -97.966933112Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.966933112, -97.966933112}
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