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Simplifying -1.8 + 0.05x + 0.0001x2 = 0 Solving -1.8 + 0.05x + 0.0001x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.0001 the coefficient of the squared term: Divide each side by '0.0001'. -18000 + 500x + x2 = 0 Move the constant term to the right: Add '18000' to each side of the equation. -18000 + 500x + 18000 + x2 = 0 + 18000 Reorder the terms: -18000 + 18000 + 500x + x2 = 0 + 18000 Combine like terms: -18000 + 18000 = 0 0 + 500x + x2 = 0 + 18000 500x + x2 = 0 + 18000 Combine like terms: 0 + 18000 = 18000 500x + x2 = 18000 The x term is 500x. Take half its coefficient (250). Square it (62500) and add it to both sides. Add '62500' to each side of the equation. 500x + 62500 + x2 = 18000 + 62500 Reorder the terms: 62500 + 500x + x2 = 18000 + 62500 Combine like terms: 18000 + 62500 = 80500 62500 + 500x + x2 = 80500 Factor a perfect square on the left side: (x + 250)(x + 250) = 80500 Calculate the square root of the right side: 283.725219182 Break this problem into two subproblems by setting (x + 250) equal to 283.725219182 and -283.725219182.Subproblem 1
x + 250 = 283.725219182 Simplifying x + 250 = 283.725219182 Reorder the terms: 250 + x = 283.725219182 Solving 250 + x = 283.725219182 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-250' to each side of the equation. 250 + -250 + x = 283.725219182 + -250 Combine like terms: 250 + -250 = 0 0 + x = 283.725219182 + -250 x = 283.725219182 + -250 Combine like terms: 283.725219182 + -250 = 33.725219182 x = 33.725219182 Simplifying x = 33.725219182Subproblem 2
x + 250 = -283.725219182 Simplifying x + 250 = -283.725219182 Reorder the terms: 250 + x = -283.725219182 Solving 250 + x = -283.725219182 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-250' to each side of the equation. 250 + -250 + x = -283.725219182 + -250 Combine like terms: 250 + -250 = 0 0 + x = -283.725219182 + -250 x = -283.725219182 + -250 Combine like terms: -283.725219182 + -250 = -533.725219182 x = -533.725219182 Simplifying x = -533.725219182Solution
The solution to the problem is based on the solutions from the subproblems. x = {33.725219182, -533.725219182}
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