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Simplifying 0.0001x2 + 0.04x + -1.5 = 0 Reorder the terms: -1.5 + 0.04x + 0.0001x2 = 0 Solving -1.5 + 0.04x + 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'. -15000 + 400x + x2 = 0 Move the constant term to the right: Add '15000' to each side of the equation. -15000 + 400x + 15000 + x2 = 0 + 15000 Reorder the terms: -15000 + 15000 + 400x + x2 = 0 + 15000 Combine like terms: -15000 + 15000 = 0 0 + 400x + x2 = 0 + 15000 400x + x2 = 0 + 15000 Combine like terms: 0 + 15000 = 15000 400x + x2 = 15000 The x term is 400x. Take half its coefficient (200). Square it (40000) and add it to both sides. Add '40000' to each side of the equation. 400x + 40000 + x2 = 15000 + 40000 Reorder the terms: 40000 + 400x + x2 = 15000 + 40000 Combine like terms: 15000 + 40000 = 55000 40000 + 400x + x2 = 55000 Factor a perfect square on the left side: (x + 200)(x + 200) = 55000 Calculate the square root of the right side: 234.520787991 Break this problem into two subproblems by setting (x + 200) equal to 234.520787991 and -234.520787991.Subproblem 1
x + 200 = 234.520787991 Simplifying x + 200 = 234.520787991 Reorder the terms: 200 + x = 234.520787991 Solving 200 + x = 234.520787991 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-200' to each side of the equation. 200 + -200 + x = 234.520787991 + -200 Combine like terms: 200 + -200 = 0 0 + x = 234.520787991 + -200 x = 234.520787991 + -200 Combine like terms: 234.520787991 + -200 = 34.520787991 x = 34.520787991 Simplifying x = 34.520787991Subproblem 2
x + 200 = -234.520787991 Simplifying x + 200 = -234.520787991 Reorder the terms: 200 + x = -234.520787991 Solving 200 + x = -234.520787991 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-200' to each side of the equation. 200 + -200 + x = -234.520787991 + -200 Combine like terms: 200 + -200 = 0 0 + x = -234.520787991 + -200 x = -234.520787991 + -200 Combine like terms: -234.520787991 + -200 = -434.520787991 x = -434.520787991 Simplifying x = -434.520787991Solution
The solution to the problem is based on the solutions from the subproblems. x = {34.520787991, -434.520787991}
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