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Simplifying 5x2 + -500x + 1875 = 0 Reorder the terms: 1875 + -500x + 5x2 = 0 Solving 1875 + -500x + 5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(375 + -100x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(375 + -100x + x2)' equal to zero and attempt to solve: Simplifying 375 + -100x + x2 = 0 Solving 375 + -100x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-375' to each side of the equation. 375 + -100x + -375 + x2 = 0 + -375 Reorder the terms: 375 + -375 + -100x + x2 = 0 + -375 Combine like terms: 375 + -375 = 0 0 + -100x + x2 = 0 + -375 -100x + x2 = 0 + -375 Combine like terms: 0 + -375 = -375 -100x + x2 = -375 The x term is -100x. Take half its coefficient (-50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. -100x + 2500 + x2 = -375 + 2500 Reorder the terms: 2500 + -100x + x2 = -375 + 2500 Combine like terms: -375 + 2500 = 2125 2500 + -100x + x2 = 2125 Factor a perfect square on the left side: (x + -50)(x + -50) = 2125 Calculate the square root of the right side: 46.097722286 Break this problem into two subproblems by setting (x + -50) equal to 46.097722286 and -46.097722286.Subproblem 1
x + -50 = 46.097722286 Simplifying x + -50 = 46.097722286 Reorder the terms: -50 + x = 46.097722286 Solving -50 + x = 46.097722286 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = 46.097722286 + 50 Combine like terms: -50 + 50 = 0 0 + x = 46.097722286 + 50 x = 46.097722286 + 50 Combine like terms: 46.097722286 + 50 = 96.097722286 x = 96.097722286 Simplifying x = 96.097722286Subproblem 2
x + -50 = -46.097722286 Simplifying x + -50 = -46.097722286 Reorder the terms: -50 + x = -46.097722286 Solving -50 + x = -46.097722286 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = -46.097722286 + 50 Combine like terms: -50 + 50 = 0 0 + x = -46.097722286 + 50 x = -46.097722286 + 50 Combine like terms: -46.097722286 + 50 = 3.902277714 x = 3.902277714 Simplifying x = 3.902277714Solution
The solution to the problem is based on the solutions from the subproblems. x = {96.097722286, 3.902277714}Solution
x = {96.097722286, 3.902277714}
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