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Simplifying 50x + -0.5x2 = 4x + 10 Reorder the terms: 50x + -0.5x2 = 10 + 4x Solving 50x + -0.5x2 = 10 + 4x Solving for variable 'x'. Reorder the terms: -10 + 50x + -4x + -0.5x2 = 10 + 4x + -10 + -4x Combine like terms: 50x + -4x = 46x -10 + 46x + -0.5x2 = 10 + 4x + -10 + -4x Reorder the terms: -10 + 46x + -0.5x2 = 10 + -10 + 4x + -4x Combine like terms: 10 + -10 = 0 -10 + 46x + -0.5x2 = 0 + 4x + -4x -10 + 46x + -0.5x2 = 4x + -4x Combine like terms: 4x + -4x = 0 -10 + 46x + -0.5x2 = 0 Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. 20 + -92x + x2 = 0 Move the constant term to the right: Add '-20' to each side of the equation. 20 + -92x + -20 + x2 = 0 + -20 Reorder the terms: 20 + -20 + -92x + x2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -92x + x2 = 0 + -20 -92x + x2 = 0 + -20 Combine like terms: 0 + -20 = -20 -92x + x2 = -20 The x term is -92x. Take half its coefficient (-46). Square it (2116) and add it to both sides. Add '2116' to each side of the equation. -92x + 2116 + x2 = -20 + 2116 Reorder the terms: 2116 + -92x + x2 = -20 + 2116 Combine like terms: -20 + 2116 = 2096 2116 + -92x + x2 = 2096 Factor a perfect square on the left side: (x + -46)(x + -46) = 2096 Calculate the square root of the right side: 45.782092569 Break this problem into two subproblems by setting (x + -46) equal to 45.782092569 and -45.782092569.Subproblem 1
x + -46 = 45.782092569 Simplifying x + -46 = 45.782092569 Reorder the terms: -46 + x = 45.782092569 Solving -46 + x = 45.782092569 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '46' to each side of the equation. -46 + 46 + x = 45.782092569 + 46 Combine like terms: -46 + 46 = 0 0 + x = 45.782092569 + 46 x = 45.782092569 + 46 Combine like terms: 45.782092569 + 46 = 91.782092569 x = 91.782092569 Simplifying x = 91.782092569Subproblem 2
x + -46 = -45.782092569 Simplifying x + -46 = -45.782092569 Reorder the terms: -46 + x = -45.782092569 Solving -46 + x = -45.782092569 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '46' to each side of the equation. -46 + 46 + x = -45.782092569 + 46 Combine like terms: -46 + 46 = 0 0 + x = -45.782092569 + 46 x = -45.782092569 + 46 Combine like terms: -45.782092569 + 46 = 0.217907431 x = 0.217907431 Simplifying x = 0.217907431Solution
The solution to the problem is based on the solutions from the subproblems. x = {91.782092569, 0.217907431}
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