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Simplifying x2 + 75x + -385 = 0 Reorder the terms: -385 + 75x + x2 = 0 Solving -385 + 75x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '385' to each side of the equation. -385 + 75x + 385 + x2 = 0 + 385 Reorder the terms: -385 + 385 + 75x + x2 = 0 + 385 Combine like terms: -385 + 385 = 0 0 + 75x + x2 = 0 + 385 75x + x2 = 0 + 385 Combine like terms: 0 + 385 = 385 75x + x2 = 385 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 = 385 + 1406.25 Reorder the terms: 1406.25 + 75x + x2 = 385 + 1406.25 Combine like terms: 385 + 1406.25 = 1791.25 1406.25 + 75x + x2 = 1791.25 Factor a perfect square on the left side: (x + 37.5)(x + 37.5) = 1791.25 Calculate the square root of the right side: 42.323161508 Break this problem into two subproblems by setting (x + 37.5) equal to 42.323161508 and -42.323161508.Subproblem 1
x + 37.5 = 42.323161508 Simplifying x + 37.5 = 42.323161508 Reorder the terms: 37.5 + x = 42.323161508 Solving 37.5 + x = 42.323161508 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 = 42.323161508 + -37.5 Combine like terms: 37.5 + -37.5 = 0.0 0.0 + x = 42.323161508 + -37.5 x = 42.323161508 + -37.5 Combine like terms: 42.323161508 + -37.5 = 4.823161508 x = 4.823161508 Simplifying x = 4.823161508Subproblem 2
x + 37.5 = -42.323161508 Simplifying x + 37.5 = -42.323161508 Reorder the terms: 37.5 + x = -42.323161508 Solving 37.5 + x = -42.323161508 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 = -42.323161508 + -37.5 Combine like terms: 37.5 + -37.5 = 0.0 0.0 + x = -42.323161508 + -37.5 x = -42.323161508 + -37.5 Combine like terms: -42.323161508 + -37.5 = -79.823161508 x = -79.823161508 Simplifying x = -79.823161508Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.823161508, -79.823161508}
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