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Simplifying x2 + 162x + 81 = 0 Reorder the terms: 81 + 162x + x2 = 0 Solving 81 + 162x + 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 + 162x + -81 + x2 = 0 + -81 Reorder the terms: 81 + -81 + 162x + x2 = 0 + -81 Combine like terms: 81 + -81 = 0 0 + 162x + x2 = 0 + -81 162x + x2 = 0 + -81 Combine like terms: 0 + -81 = -81 162x + x2 = -81 The x term is 162x. Take half its coefficient (81). Square it (6561) and add it to both sides. Add '6561' to each side of the equation. 162x + 6561 + x2 = -81 + 6561 Reorder the terms: 6561 + 162x + x2 = -81 + 6561 Combine like terms: -81 + 6561 = 6480 6561 + 162x + x2 = 6480 Factor a perfect square on the left side: (x + 81)(x + 81) = 6480 Calculate the square root of the right side: 80.49844719 Break this problem into two subproblems by setting (x + 81) equal to 80.49844719 and -80.49844719.Subproblem 1
x + 81 = 80.49844719 Simplifying x + 81 = 80.49844719 Reorder the terms: 81 + x = 80.49844719 Solving 81 + x = 80.49844719 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-81' to each side of the equation. 81 + -81 + x = 80.49844719 + -81 Combine like terms: 81 + -81 = 0 0 + x = 80.49844719 + -81 x = 80.49844719 + -81 Combine like terms: 80.49844719 + -81 = -0.50155281 x = -0.50155281 Simplifying x = -0.50155281Subproblem 2
x + 81 = -80.49844719 Simplifying x + 81 = -80.49844719 Reorder the terms: 81 + x = -80.49844719 Solving 81 + x = -80.49844719 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-81' to each side of the equation. 81 + -81 + x = -80.49844719 + -81 Combine like terms: 81 + -81 = 0 0 + x = -80.49844719 + -81 x = -80.49844719 + -81 Combine like terms: -80.49844719 + -81 = -161.49844719 x = -161.49844719 Simplifying x = -161.49844719Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.50155281, -161.49844719}
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