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Simplifying -0.05x2 + 15x + -250 = 0 Reorder the terms: -250 + 15x + -0.05x2 = 0 Solving -250 + 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'. 5000 + -300x + x2 = 0 Move the constant term to the right: Add '-5000' to each side of the equation. 5000 + -300x + -5000 + x2 = 0 + -5000 Reorder the terms: 5000 + -5000 + -300x + x2 = 0 + -5000 Combine like terms: 5000 + -5000 = 0 0 + -300x + x2 = 0 + -5000 -300x + x2 = 0 + -5000 Combine like terms: 0 + -5000 = -5000 -300x + x2 = -5000 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 = -5000 + 22500 Reorder the terms: 22500 + -300x + x2 = -5000 + 22500 Combine like terms: -5000 + 22500 = 17500 22500 + -300x + x2 = 17500 Factor a perfect square on the left side: (x + -150)(x + -150) = 17500 Calculate the square root of the right side: 132.287565553 Break this problem into two subproblems by setting (x + -150) equal to 132.287565553 and -132.287565553.Subproblem 1
x + -150 = 132.287565553 Simplifying x + -150 = 132.287565553 Reorder the terms: -150 + x = 132.287565553 Solving -150 + x = 132.287565553 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 = 132.287565553 + 150 Combine like terms: -150 + 150 = 0 0 + x = 132.287565553 + 150 x = 132.287565553 + 150 Combine like terms: 132.287565553 + 150 = 282.287565553 x = 282.287565553 Simplifying x = 282.287565553Subproblem 2
x + -150 = -132.287565553 Simplifying x + -150 = -132.287565553 Reorder the terms: -150 + x = -132.287565553 Solving -150 + x = -132.287565553 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 = -132.287565553 + 150 Combine like terms: -150 + 150 = 0 0 + x = -132.287565553 + 150 x = -132.287565553 + 150 Combine like terms: -132.287565553 + 150 = 17.712434447 x = 17.712434447 Simplifying x = 17.712434447Solution
The solution to the problem is based on the solutions from the subproblems. x = {282.287565553, 17.712434447}
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