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Simplifying 0.02x2 + -5x + -12500 = 0 Reorder the terms: -12500 + -5x + 0.02x2 = 0 Solving -12500 + -5x + 0.02x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.02 the coefficient of the squared term: Divide each side by '0.02'. -625000 + -250x + x2 = 0 Move the constant term to the right: Add '625000' to each side of the equation. -625000 + -250x + 625000 + x2 = 0 + 625000 Reorder the terms: -625000 + 625000 + -250x + x2 = 0 + 625000 Combine like terms: -625000 + 625000 = 0 0 + -250x + x2 = 0 + 625000 -250x + x2 = 0 + 625000 Combine like terms: 0 + 625000 = 625000 -250x + x2 = 625000 The x term is -250x. Take half its coefficient (-125). Square it (15625) and add it to both sides. Add '15625' to each side of the equation. -250x + 15625 + x2 = 625000 + 15625 Reorder the terms: 15625 + -250x + x2 = 625000 + 15625 Combine like terms: 625000 + 15625 = 640625 15625 + -250x + x2 = 640625 Factor a perfect square on the left side: (x + -125)(x + -125) = 640625 Calculate the square root of the right side: 800.390529679 Break this problem into two subproblems by setting (x + -125) equal to 800.390529679 and -800.390529679.Subproblem 1
x + -125 = 800.390529679 Simplifying x + -125 = 800.390529679 Reorder the terms: -125 + x = 800.390529679 Solving -125 + x = 800.390529679 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '125' to each side of the equation. -125 + 125 + x = 800.390529679 + 125 Combine like terms: -125 + 125 = 0 0 + x = 800.390529679 + 125 x = 800.390529679 + 125 Combine like terms: 800.390529679 + 125 = 925.390529679 x = 925.390529679 Simplifying x = 925.390529679Subproblem 2
x + -125 = -800.390529679 Simplifying x + -125 = -800.390529679 Reorder the terms: -125 + x = -800.390529679 Solving -125 + x = -800.390529679 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '125' to each side of the equation. -125 + 125 + x = -800.390529679 + 125 Combine like terms: -125 + 125 = 0 0 + x = -800.390529679 + 125 x = -800.390529679 + 125 Combine like terms: -800.390529679 + 125 = -675.390529679 x = -675.390529679 Simplifying x = -675.390529679Solution
The solution to the problem is based on the solutions from the subproblems. x = {925.390529679, -675.390529679}
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