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Simplifying x2 + -75x + 24 = 0 Reorder the terms: 24 + -75x + x2 = 0 Solving 24 + -75x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-24' to each side of the equation. 24 + -75x + -24 + x2 = 0 + -24 Reorder the terms: 24 + -24 + -75x + x2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + -75x + x2 = 0 + -24 -75x + x2 = 0 + -24 Combine like terms: 0 + -24 = -24 -75x + x2 = -24 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 = -24 + 1406.25 Reorder the terms: 1406.25 + -75x + x2 = -24 + 1406.25 Combine like terms: -24 + 1406.25 = 1382.25 1406.25 + -75x + x2 = 1382.25 Factor a perfect square on the left side: (x + -37.5)(x + -37.5) = 1382.25 Calculate the square root of the right side: 37.17862289 Break this problem into two subproblems by setting (x + -37.5) equal to 37.17862289 and -37.17862289.Subproblem 1
x + -37.5 = 37.17862289 Simplifying x + -37.5 = 37.17862289 Reorder the terms: -37.5 + x = 37.17862289 Solving -37.5 + x = 37.17862289 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 = 37.17862289 + 37.5 Combine like terms: -37.5 + 37.5 = 0.0 0.0 + x = 37.17862289 + 37.5 x = 37.17862289 + 37.5 Combine like terms: 37.17862289 + 37.5 = 74.67862289 x = 74.67862289 Simplifying x = 74.67862289Subproblem 2
x + -37.5 = -37.17862289 Simplifying x + -37.5 = -37.17862289 Reorder the terms: -37.5 + x = -37.17862289 Solving -37.5 + x = -37.17862289 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 = -37.17862289 + 37.5 Combine like terms: -37.5 + 37.5 = 0.0 0.0 + x = -37.17862289 + 37.5 x = -37.17862289 + 37.5 Combine like terms: -37.17862289 + 37.5 = 0.32137711 x = 0.32137711 Simplifying x = 0.32137711Solution
The solution to the problem is based on the solutions from the subproblems. x = {74.67862289, 0.32137711}
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