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Simplifying 2x(13 + x) = 41 + x (13 * 2x + x * 2x) = 41 + x (26x + 2x2) = 41 + x Solving 26x + 2x2 = 41 + x Solving for variable 'x'. Reorder the terms: -41 + 26x + -1x + 2x2 = 41 + x + -41 + -1x Combine like terms: 26x + -1x = 25x -41 + 25x + 2x2 = 41 + x + -41 + -1x Reorder the terms: -41 + 25x + 2x2 = 41 + -41 + x + -1x Combine like terms: 41 + -41 = 0 -41 + 25x + 2x2 = 0 + x + -1x -41 + 25x + 2x2 = x + -1x Combine like terms: x + -1x = 0 -41 + 25x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -20.5 + 12.5x + x2 = 0 Move the constant term to the right: Add '20.5' to each side of the equation. -20.5 + 12.5x + 20.5 + x2 = 0 + 20.5 Reorder the terms: -20.5 + 20.5 + 12.5x + x2 = 0 + 20.5 Combine like terms: -20.5 + 20.5 = 0.0 0.0 + 12.5x + x2 = 0 + 20.5 12.5x + x2 = 0 + 20.5 Combine like terms: 0 + 20.5 = 20.5 12.5x + x2 = 20.5 The x term is 12.5x. Take half its coefficient (6.25). Square it (39.0625) and add it to both sides. Add '39.0625' to each side of the equation. 12.5x + 39.0625 + x2 = 20.5 + 39.0625 Reorder the terms: 39.0625 + 12.5x + x2 = 20.5 + 39.0625 Combine like terms: 20.5 + 39.0625 = 59.5625 39.0625 + 12.5x + x2 = 59.5625 Factor a perfect square on the left side: (x + 6.25)(x + 6.25) = 59.5625 Calculate the square root of the right side: 7.71767452 Break this problem into two subproblems by setting (x + 6.25) equal to 7.71767452 and -7.71767452.Subproblem 1
x + 6.25 = 7.71767452 Simplifying x + 6.25 = 7.71767452 Reorder the terms: 6.25 + x = 7.71767452 Solving 6.25 + x = 7.71767452 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.25' to each side of the equation. 6.25 + -6.25 + x = 7.71767452 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + x = 7.71767452 + -6.25 x = 7.71767452 + -6.25 Combine like terms: 7.71767452 + -6.25 = 1.46767452 x = 1.46767452 Simplifying x = 1.46767452Subproblem 2
x + 6.25 = -7.71767452 Simplifying x + 6.25 = -7.71767452 Reorder the terms: 6.25 + x = -7.71767452 Solving 6.25 + x = -7.71767452 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.25' to each side of the equation. 6.25 + -6.25 + x = -7.71767452 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + x = -7.71767452 + -6.25 x = -7.71767452 + -6.25 Combine like terms: -7.71767452 + -6.25 = -13.96767452 x = -13.96767452 Simplifying x = -13.96767452Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.46767452, -13.96767452}
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