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Simplifying 98(x) + -1x2 + -7.96 = 0 Reorder the terms: -7.96 + 98x + -1x2 = 0 Solving -7.96 + 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'. 7.96 + -98x + x2 = 0 Move the constant term to the right: Add '-7.96' to each side of the equation. 7.96 + -98x + -7.96 + x2 = 0 + -7.96 Reorder the terms: 7.96 + -7.96 + -98x + x2 = 0 + -7.96 Combine like terms: 7.96 + -7.96 = 0.00 0.00 + -98x + x2 = 0 + -7.96 -98x + x2 = 0 + -7.96 Combine like terms: 0 + -7.96 = -7.96 -98x + x2 = -7.96 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 = -7.96 + 2401 Reorder the terms: 2401 + -98x + x2 = -7.96 + 2401 Combine like terms: -7.96 + 2401 = 2393.04 2401 + -98x + x2 = 2393.04 Factor a perfect square on the left side: (x + -49)(x + -49) = 2393.04 Calculate the square root of the right side: 48.918708078 Break this problem into two subproblems by setting (x + -49) equal to 48.918708078 and -48.918708078.Subproblem 1
x + -49 = 48.918708078 Simplifying x + -49 = 48.918708078 Reorder the terms: -49 + x = 48.918708078 Solving -49 + x = 48.918708078 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 = 48.918708078 + 49 Combine like terms: -49 + 49 = 0 0 + x = 48.918708078 + 49 x = 48.918708078 + 49 Combine like terms: 48.918708078 + 49 = 97.918708078 x = 97.918708078 Simplifying x = 97.918708078Subproblem 2
x + -49 = -48.918708078 Simplifying x + -49 = -48.918708078 Reorder the terms: -49 + x = -48.918708078 Solving -49 + x = -48.918708078 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 = -48.918708078 + 49 Combine like terms: -49 + 49 = 0 0 + x = -48.918708078 + 49 x = -48.918708078 + 49 Combine like terms: -48.918708078 + 49 = 0.081291922 x = 0.081291922 Simplifying x = 0.081291922Solution
The solution to the problem is based on the solutions from the subproblems. x = {97.918708078, 0.081291922}
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