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Simplifying 0.5x2 + 50x + -5000 = 0 Reorder the terms: -5000 + 50x + 0.5x2 = 0 Solving -5000 + 50x + 0.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -10000 + 100x + x2 = 0 Move the constant term to the right: Add '10000' to each side of the equation. -10000 + 100x + 10000 + x2 = 0 + 10000 Reorder the terms: -10000 + 10000 + 100x + x2 = 0 + 10000 Combine like terms: -10000 + 10000 = 0 0 + 100x + x2 = 0 + 10000 100x + x2 = 0 + 10000 Combine like terms: 0 + 10000 = 10000 100x + x2 = 10000 The x term is 100x. Take half its coefficient (50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. 100x + 2500 + x2 = 10000 + 2500 Reorder the terms: 2500 + 100x + x2 = 10000 + 2500 Combine like terms: 10000 + 2500 = 12500 2500 + 100x + x2 = 12500 Factor a perfect square on the left side: (x + 50)(x + 50) = 12500 Calculate the square root of the right side: 111.803398875 Break this problem into two subproblems by setting (x + 50) equal to 111.803398875 and -111.803398875.Subproblem 1
x + 50 = 111.803398875 Simplifying x + 50 = 111.803398875 Reorder the terms: 50 + x = 111.803398875 Solving 50 + x = 111.803398875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + x = 111.803398875 + -50 Combine like terms: 50 + -50 = 0 0 + x = 111.803398875 + -50 x = 111.803398875 + -50 Combine like terms: 111.803398875 + -50 = 61.803398875 x = 61.803398875 Simplifying x = 61.803398875Subproblem 2
x + 50 = -111.803398875 Simplifying x + 50 = -111.803398875 Reorder the terms: 50 + x = -111.803398875 Solving 50 + x = -111.803398875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + x = -111.803398875 + -50 Combine like terms: 50 + -50 = 0 0 + x = -111.803398875 + -50 x = -111.803398875 + -50 Combine like terms: -111.803398875 + -50 = -161.803398875 x = -161.803398875 Simplifying x = -161.803398875Solution
The solution to the problem is based on the solutions from the subproblems. x = {61.803398875, -161.803398875}
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