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Simplifying 2x2 + -197x + 20 = 0 Reorder the terms: 20 + -197x + 2x2 = 0 Solving 20 + -197x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 10 + -98.5x + x2 = 0 Move the constant term to the right: Add '-10' to each side of the equation. 10 + -98.5x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + -98.5x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -98.5x + x2 = 0 + -10 -98.5x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 -98.5x + x2 = -10 The x term is -98.5x. Take half its coefficient (-49.25). Square it (2425.5625) and add it to both sides. Add '2425.5625' to each side of the equation. -98.5x + 2425.5625 + x2 = -10 + 2425.5625 Reorder the terms: 2425.5625 + -98.5x + x2 = -10 + 2425.5625 Combine like terms: -10 + 2425.5625 = 2415.5625 2425.5625 + -98.5x + x2 = 2415.5625 Factor a perfect square on the left side: (x + -49.25)(x + -49.25) = 2415.5625 Calculate the square root of the right side: 49.148372303 Break this problem into two subproblems by setting (x + -49.25) equal to 49.148372303 and -49.148372303.Subproblem 1
x + -49.25 = 49.148372303 Simplifying x + -49.25 = 49.148372303 Reorder the terms: -49.25 + x = 49.148372303 Solving -49.25 + x = 49.148372303 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '49.25' to each side of the equation. -49.25 + 49.25 + x = 49.148372303 + 49.25 Combine like terms: -49.25 + 49.25 = 0.00 0.00 + x = 49.148372303 + 49.25 x = 49.148372303 + 49.25 Combine like terms: 49.148372303 + 49.25 = 98.398372303 x = 98.398372303 Simplifying x = 98.398372303Subproblem 2
x + -49.25 = -49.148372303 Simplifying x + -49.25 = -49.148372303 Reorder the terms: -49.25 + x = -49.148372303 Solving -49.25 + x = -49.148372303 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '49.25' to each side of the equation. -49.25 + 49.25 + x = -49.148372303 + 49.25 Combine like terms: -49.25 + 49.25 = 0.00 0.00 + x = -49.148372303 + 49.25 x = -49.148372303 + 49.25 Combine like terms: -49.148372303 + 49.25 = 0.101627697 x = 0.101627697 Simplifying x = 0.101627697Solution
The solution to the problem is based on the solutions from the subproblems. x = {98.398372303, 0.101627697}
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