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Simplifying (x) = x2 + -20x + 41 x = x2 + -20x + 41 Reorder the terms: x = 41 + -20x + x2 Solving x = 41 + -20x + x2 Solving for variable 'x'. Reorder the terms: -41 + x + 20x + -1x2 = 41 + -20x + x2 + -41 + 20x + -1x2 Combine like terms: x + 20x = 21x -41 + 21x + -1x2 = 41 + -20x + x2 + -41 + 20x + -1x2 Reorder the terms: -41 + 21x + -1x2 = 41 + -41 + -20x + 20x + x2 + -1x2 Combine like terms: 41 + -41 = 0 -41 + 21x + -1x2 = 0 + -20x + 20x + x2 + -1x2 -41 + 21x + -1x2 = -20x + 20x + x2 + -1x2 Combine like terms: -20x + 20x = 0 -41 + 21x + -1x2 = 0 + x2 + -1x2 -41 + 21x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -41 + 21x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 41 + -21x + x2 = 0 Move the constant term to the right: Add '-41' to each side of the equation. 41 + -21x + -41 + x2 = 0 + -41 Reorder the terms: 41 + -41 + -21x + x2 = 0 + -41 Combine like terms: 41 + -41 = 0 0 + -21x + x2 = 0 + -41 -21x + x2 = 0 + -41 Combine like terms: 0 + -41 = -41 -21x + x2 = -41 The x term is -21x. Take half its coefficient (-10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. -21x + 110.25 + x2 = -41 + 110.25 Reorder the terms: 110.25 + -21x + x2 = -41 + 110.25 Combine like terms: -41 + 110.25 = 69.25 110.25 + -21x + x2 = 69.25 Factor a perfect square on the left side: (x + -10.5)(x + -10.5) = 69.25 Calculate the square root of the right side: 8.321658489 Break this problem into two subproblems by setting (x + -10.5) equal to 8.321658489 and -8.321658489.Subproblem 1
x + -10.5 = 8.321658489 Simplifying x + -10.5 = 8.321658489 Reorder the terms: -10.5 + x = 8.321658489 Solving -10.5 + x = 8.321658489 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + x = 8.321658489 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = 8.321658489 + 10.5 x = 8.321658489 + 10.5 Combine like terms: 8.321658489 + 10.5 = 18.821658489 x = 18.821658489 Simplifying x = 18.821658489Subproblem 2
x + -10.5 = -8.321658489 Simplifying x + -10.5 = -8.321658489 Reorder the terms: -10.5 + x = -8.321658489 Solving -10.5 + x = -8.321658489 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + x = -8.321658489 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = -8.321658489 + 10.5 x = -8.321658489 + 10.5 Combine like terms: -8.321658489 + 10.5 = 2.178341511 x = 2.178341511 Simplifying x = 2.178341511Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.821658489, 2.178341511}
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