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Simplifying 0.05x2 + 15x + 500 = 0 Reorder the terms: 500 + 15x + 0.05x2 = 0 Solving 500 + 15x + 0.05x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.05 the coefficient of the squared term: Divide each side by '0.05'. 10000 + 300x + x2 = 0 Move the constant term to the right: Add '-10000' to each side of the equation. 10000 + 300x + -10000 + x2 = 0 + -10000 Reorder the terms: 10000 + -10000 + 300x + x2 = 0 + -10000 Combine like terms: 10000 + -10000 = 0 0 + 300x + x2 = 0 + -10000 300x + x2 = 0 + -10000 Combine like terms: 0 + -10000 = -10000 300x + x2 = -10000 The x term is 300x. Take half its coefficient (150). Square it (22500) and add it to both sides. Add '22500' to each side of the equation. 300x + 22500 + x2 = -10000 + 22500 Reorder the terms: 22500 + 300x + x2 = -10000 + 22500 Combine like terms: -10000 + 22500 = 12500 22500 + 300x + x2 = 12500 Factor a perfect square on the left side: (x + 150)(x + 150) = 12500 Calculate the square root of the right side: 111.803398875 Break this problem into two subproblems by setting (x + 150) equal to 111.803398875 and -111.803398875.Subproblem 1
x + 150 = 111.803398875 Simplifying x + 150 = 111.803398875 Reorder the terms: 150 + x = 111.803398875 Solving 150 + x = 111.803398875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-150' to each side of the equation. 150 + -150 + x = 111.803398875 + -150 Combine like terms: 150 + -150 = 0 0 + x = 111.803398875 + -150 x = 111.803398875 + -150 Combine like terms: 111.803398875 + -150 = -38.196601125 x = -38.196601125 Simplifying x = -38.196601125Subproblem 2
x + 150 = -111.803398875 Simplifying x + 150 = -111.803398875 Reorder the terms: 150 + x = -111.803398875 Solving 150 + x = -111.803398875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-150' to each side of the equation. 150 + -150 + x = -111.803398875 + -150 Combine like terms: 150 + -150 = 0 0 + x = -111.803398875 + -150 x = -111.803398875 + -150 Combine like terms: -111.803398875 + -150 = -261.803398875 x = -261.803398875 Simplifying x = -261.803398875Solution
The solution to the problem is based on the solutions from the subproblems. x = {-38.196601125, -261.803398875}
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