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Simplifying 10x + 300 = -0.2x2 + 50x Reorder the terms: 300 + 10x = -0.2x2 + 50x Reorder the terms: 300 + 10x = 50x + -0.2x2 Solving 300 + 10x = 50x + -0.2x2 Solving for variable 'x'. Combine like terms: 10x + -50x = -40x 300 + -40x + 0.2x2 = 50x + -0.2x2 + -50x + 0.2x2 Reorder the terms: 300 + -40x + 0.2x2 = 50x + -50x + -0.2x2 + 0.2x2 Combine like terms: 50x + -50x = 0 300 + -40x + 0.2x2 = 0 + -0.2x2 + 0.2x2 300 + -40x + 0.2x2 = -0.2x2 + 0.2x2 Combine like terms: -0.2x2 + 0.2x2 = 0.0 300 + -40x + 0.2x2 = 0.0 Begin completing the square. Divide all terms by 0.2 the coefficient of the squared term: Divide each side by '0.2'. 1500 + -200x + x2 = 0 Move the constant term to the right: Add '-1500' to each side of the equation. 1500 + -200x + -1500 + x2 = 0 + -1500 Reorder the terms: 1500 + -1500 + -200x + x2 = 0 + -1500 Combine like terms: 1500 + -1500 = 0 0 + -200x + x2 = 0 + -1500 -200x + x2 = 0 + -1500 Combine like terms: 0 + -1500 = -1500 -200x + x2 = -1500 The x term is -200x. Take half its coefficient (-100). Square it (10000) and add it to both sides. Add '10000' to each side of the equation. -200x + 10000 + x2 = -1500 + 10000 Reorder the terms: 10000 + -200x + x2 = -1500 + 10000 Combine like terms: -1500 + 10000 = 8500 10000 + -200x + x2 = 8500 Factor a perfect square on the left side: (x + -100)(x + -100) = 8500 Calculate the square root of the right side: 92.195444573 Break this problem into two subproblems by setting (x + -100) equal to 92.195444573 and -92.195444573.Subproblem 1
x + -100 = 92.195444573 Simplifying x + -100 = 92.195444573 Reorder the terms: -100 + x = 92.195444573 Solving -100 + x = 92.195444573 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + x = 92.195444573 + 100 Combine like terms: -100 + 100 = 0 0 + x = 92.195444573 + 100 x = 92.195444573 + 100 Combine like terms: 92.195444573 + 100 = 192.195444573 x = 192.195444573 Simplifying x = 192.195444573Subproblem 2
x + -100 = -92.195444573 Simplifying x + -100 = -92.195444573 Reorder the terms: -100 + x = -92.195444573 Solving -100 + x = -92.195444573 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + x = -92.195444573 + 100 Combine like terms: -100 + 100 = 0 0 + x = -92.195444573 + 100 x = -92.195444573 + 100 Combine like terms: -92.195444573 + 100 = 7.804555427 x = 7.804555427 Simplifying x = 7.804555427Solution
The solution to the problem is based on the solutions from the subproblems. x = {192.195444573, 7.804555427}
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