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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 = 675.390529679 x = 675.390529679 Simplifying x = 675.390529679Subproblem 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 = -925.390529679 x = -925.390529679 Simplifying x = -925.390529679Solution
The solution to the problem is based on the solutions from the subproblems. x = {675.390529679, -925.390529679}
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