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Simplifying -0.5x2 + 100x + -2450 = 0 Reorder the terms: -2450 + 100x + -0.5x2 = 0 Solving -2450 + 100x + -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'. 4900 + -200x + x2 = 0 Move the constant term to the right: Add '-4900' to each side of the equation. 4900 + -200x + -4900 + x2 = 0 + -4900 Reorder the terms: 4900 + -4900 + -200x + x2 = 0 + -4900 Combine like terms: 4900 + -4900 = 0 0 + -200x + x2 = 0 + -4900 -200x + x2 = 0 + -4900 Combine like terms: 0 + -4900 = -4900 -200x + x2 = -4900 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 = -4900 + 10000 Reorder the terms: 10000 + -200x + x2 = -4900 + 10000 Combine like terms: -4900 + 10000 = 5100 10000 + -200x + x2 = 5100 Factor a perfect square on the left side: (x + -100)(x + -100) = 5100 Calculate the square root of the right side: 71.414284285 Break this problem into two subproblems by setting (x + -100) equal to 71.414284285 and -71.414284285.Subproblem 1
x + -100 = 71.414284285 Simplifying x + -100 = 71.414284285 Reorder the terms: -100 + x = 71.414284285 Solving -100 + x = 71.414284285 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 = 71.414284285 + 100 Combine like terms: -100 + 100 = 0 0 + x = 71.414284285 + 100 x = 71.414284285 + 100 Combine like terms: 71.414284285 + 100 = 171.414284285 x = 171.414284285 Simplifying x = 171.414284285Subproblem 2
x + -100 = -71.414284285 Simplifying x + -100 = -71.414284285 Reorder the terms: -100 + x = -71.414284285 Solving -100 + x = -71.414284285 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 = -71.414284285 + 100 Combine like terms: -100 + 100 = 0 0 + x = -71.414284285 + 100 x = -71.414284285 + 100 Combine like terms: -71.414284285 + 100 = 28.585715715 x = 28.585715715 Simplifying x = 28.585715715Solution
The solution to the problem is based on the solutions from the subproblems. x = {171.414284285, 28.585715715}
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