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Simplifying x2 + 46x + 81 = 0 Reorder the terms: 81 + 46x + x2 = 0 Solving 81 + 46x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-81' to each side of the equation. 81 + 46x + -81 + x2 = 0 + -81 Reorder the terms: 81 + -81 + 46x + x2 = 0 + -81 Combine like terms: 81 + -81 = 0 0 + 46x + x2 = 0 + -81 46x + x2 = 0 + -81 Combine like terms: 0 + -81 = -81 46x + x2 = -81 The x term is 46x. Take half its coefficient (23). Square it (529) and add it to both sides. Add '529' to each side of the equation. 46x + 529 + x2 = -81 + 529 Reorder the terms: 529 + 46x + x2 = -81 + 529 Combine like terms: -81 + 529 = 448 529 + 46x + x2 = 448 Factor a perfect square on the left side: (x + 23)(x + 23) = 448 Calculate the square root of the right side: 21.166010489 Break this problem into two subproblems by setting (x + 23) equal to 21.166010489 and -21.166010489.Subproblem 1
x + 23 = 21.166010489 Simplifying x + 23 = 21.166010489 Reorder the terms: 23 + x = 21.166010489 Solving 23 + x = 21.166010489 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-23' to each side of the equation. 23 + -23 + x = 21.166010489 + -23 Combine like terms: 23 + -23 = 0 0 + x = 21.166010489 + -23 x = 21.166010489 + -23 Combine like terms: 21.166010489 + -23 = -1.833989511 x = -1.833989511 Simplifying x = -1.833989511Subproblem 2
x + 23 = -21.166010489 Simplifying x + 23 = -21.166010489 Reorder the terms: 23 + x = -21.166010489 Solving 23 + x = -21.166010489 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-23' to each side of the equation. 23 + -23 + x = -21.166010489 + -23 Combine like terms: 23 + -23 = 0 0 + x = -21.166010489 + -23 x = -21.166010489 + -23 Combine like terms: -21.166010489 + -23 = -44.166010489 x = -44.166010489 Simplifying x = -44.166010489Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.833989511, -44.166010489}
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