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Simplifying 0.04x2 + 140x + 15000 = 0 Reorder the terms: 15000 + 140x + 0.04x2 = 0 Solving 15000 + 140x + 0.04x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.04 the coefficient of the squared term: Divide each side by '0.04'. 375000 + 3500x + x2 = 0 Move the constant term to the right: Add '-375000' to each side of the equation. 375000 + 3500x + -375000 + x2 = 0 + -375000 Reorder the terms: 375000 + -375000 + 3500x + x2 = 0 + -375000 Combine like terms: 375000 + -375000 = 0 0 + 3500x + x2 = 0 + -375000 3500x + x2 = 0 + -375000 Combine like terms: 0 + -375000 = -375000 3500x + x2 = -375000 The x term is 3500x. Take half its coefficient (1750). Square it (3062500) and add it to both sides. Add '3062500' to each side of the equation. 3500x + 3062500 + x2 = -375000 + 3062500 Reorder the terms: 3062500 + 3500x + x2 = -375000 + 3062500 Combine like terms: -375000 + 3062500 = 2687500 3062500 + 3500x + x2 = 2687500 Factor a perfect square on the left side: (x + 1750)(x + 1750) = 2687500 Calculate the square root of the right side: 1639.359631076 Break this problem into two subproblems by setting (x + 1750) equal to 1639.359631076 and -1639.359631076.Subproblem 1
x + 1750 = 1639.359631076 Simplifying x + 1750 = 1639.359631076 Reorder the terms: 1750 + x = 1639.359631076 Solving 1750 + x = 1639.359631076 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1750' to each side of the equation. 1750 + -1750 + x = 1639.359631076 + -1750 Combine like terms: 1750 + -1750 = 0 0 + x = 1639.359631076 + -1750 x = 1639.359631076 + -1750 Combine like terms: 1639.359631076 + -1750 = -110.640368924 x = -110.640368924 Simplifying x = -110.640368924Subproblem 2
x + 1750 = -1639.359631076 Simplifying x + 1750 = -1639.359631076 Reorder the terms: 1750 + x = -1639.359631076 Solving 1750 + x = -1639.359631076 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1750' to each side of the equation. 1750 + -1750 + x = -1639.359631076 + -1750 Combine like terms: 1750 + -1750 = 0 0 + x = -1639.359631076 + -1750 x = -1639.359631076 + -1750 Combine like terms: -1639.359631076 + -1750 = -3389.359631076 x = -3389.359631076 Simplifying x = -3389.359631076Solution
The solution to the problem is based on the solutions from the subproblems. x = {-110.640368924, -3389.359631076}
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