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Simplifying -2x2 + x2 + 98x + -49 = 0 Reorder the terms: -49 + 98x + -2x2 + x2 = 0 Combine like terms: -2x2 + x2 = -1x2 -49 + 98x + -1x2 = 0 Solving -49 + 98x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 49 + -98x + x2 = 0 Move the constant term to the right: Add '-49' to each side of the equation. 49 + -98x + -49 + x2 = 0 + -49 Reorder the terms: 49 + -49 + -98x + x2 = 0 + -49 Combine like terms: 49 + -49 = 0 0 + -98x + x2 = 0 + -49 -98x + x2 = 0 + -49 Combine like terms: 0 + -49 = -49 -98x + x2 = -49 The x term is -98x. Take half its coefficient (-49). Square it (2401) and add it to both sides. Add '2401' to each side of the equation. -98x + 2401 + x2 = -49 + 2401 Reorder the terms: 2401 + -98x + x2 = -49 + 2401 Combine like terms: -49 + 2401 = 2352 2401 + -98x + x2 = 2352 Factor a perfect square on the left side: (x + -49)(x + -49) = 2352 Calculate the square root of the right side: 48.497422612 Break this problem into two subproblems by setting (x + -49) equal to 48.497422612 and -48.497422612.Subproblem 1
x + -49 = 48.497422612 Simplifying x + -49 = 48.497422612 Reorder the terms: -49 + x = 48.497422612 Solving -49 + x = 48.497422612 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '49' to each side of the equation. -49 + 49 + x = 48.497422612 + 49 Combine like terms: -49 + 49 = 0 0 + x = 48.497422612 + 49 x = 48.497422612 + 49 Combine like terms: 48.497422612 + 49 = 97.497422612 x = 97.497422612 Simplifying x = 97.497422612Subproblem 2
x + -49 = -48.497422612 Simplifying x + -49 = -48.497422612 Reorder the terms: -49 + x = -48.497422612 Solving -49 + x = -48.497422612 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '49' to each side of the equation. -49 + 49 + x = -48.497422612 + 49 Combine like terms: -49 + 49 = 0 0 + x = -48.497422612 + 49 x = -48.497422612 + 49 Combine like terms: -48.497422612 + 49 = 0.502577388 x = 0.502577388 Simplifying x = 0.502577388Solution
The solution to the problem is based on the solutions from the subproblems. x = {97.497422612, 0.502577388}
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