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Simplifying x2 + 81x + -49 = 0 Reorder the terms: -49 + 81x + x2 = 0 Solving -49 + 81x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '49' to each side of the equation. -49 + 81x + 49 + x2 = 0 + 49 Reorder the terms: -49 + 49 + 81x + x2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + 81x + x2 = 0 + 49 81x + x2 = 0 + 49 Combine like terms: 0 + 49 = 49 81x + x2 = 49 The x term is 81x. Take half its coefficient (40.5). Square it (1640.25) and add it to both sides. Add '1640.25' to each side of the equation. 81x + 1640.25 + x2 = 49 + 1640.25 Reorder the terms: 1640.25 + 81x + x2 = 49 + 1640.25 Combine like terms: 49 + 1640.25 = 1689.25 1640.25 + 81x + x2 = 1689.25 Factor a perfect square on the left side: (x + 40.5)(x + 40.5) = 1689.25 Calculate the square root of the right side: 41.100486615 Break this problem into two subproblems by setting (x + 40.5) equal to 41.100486615 and -41.100486615.Subproblem 1
x + 40.5 = 41.100486615 Simplifying x + 40.5 = 41.100486615 Reorder the terms: 40.5 + x = 41.100486615 Solving 40.5 + x = 41.100486615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-40.5' to each side of the equation. 40.5 + -40.5 + x = 41.100486615 + -40.5 Combine like terms: 40.5 + -40.5 = 0.0 0.0 + x = 41.100486615 + -40.5 x = 41.100486615 + -40.5 Combine like terms: 41.100486615 + -40.5 = 0.600486615 x = 0.600486615 Simplifying x = 0.600486615Subproblem 2
x + 40.5 = -41.100486615 Simplifying x + 40.5 = -41.100486615 Reorder the terms: 40.5 + x = -41.100486615 Solving 40.5 + x = -41.100486615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-40.5' to each side of the equation. 40.5 + -40.5 + x = -41.100486615 + -40.5 Combine like terms: 40.5 + -40.5 = 0.0 0.0 + x = -41.100486615 + -40.5 x = -41.100486615 + -40.5 Combine like terms: -41.100486615 + -40.5 = -81.600486615 x = -81.600486615 Simplifying x = -81.600486615Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.600486615, -81.600486615}
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