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Simplifying x2 + -27x + 81 = 0 Reorder the terms: 81 + -27x + x2 = 0 Solving 81 + -27x + 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 + -27x + -81 + x2 = 0 + -81 Reorder the terms: 81 + -81 + -27x + x2 = 0 + -81 Combine like terms: 81 + -81 = 0 0 + -27x + x2 = 0 + -81 -27x + x2 = 0 + -81 Combine like terms: 0 + -81 = -81 -27x + x2 = -81 The x term is -27x. Take half its coefficient (-13.5). Square it (182.25) and add it to both sides. Add '182.25' to each side of the equation. -27x + 182.25 + x2 = -81 + 182.25 Reorder the terms: 182.25 + -27x + x2 = -81 + 182.25 Combine like terms: -81 + 182.25 = 101.25 182.25 + -27x + x2 = 101.25 Factor a perfect square on the left side: (x + -13.5)(x + -13.5) = 101.25 Calculate the square root of the right side: 10.062305899 Break this problem into two subproblems by setting (x + -13.5) equal to 10.062305899 and -10.062305899.Subproblem 1
x + -13.5 = 10.062305899 Simplifying x + -13.5 = 10.062305899 Reorder the terms: -13.5 + x = 10.062305899 Solving -13.5 + x = 10.062305899 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.5' to each side of the equation. -13.5 + 13.5 + x = 10.062305899 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + x = 10.062305899 + 13.5 x = 10.062305899 + 13.5 Combine like terms: 10.062305899 + 13.5 = 23.562305899 x = 23.562305899 Simplifying x = 23.562305899Subproblem 2
x + -13.5 = -10.062305899 Simplifying x + -13.5 = -10.062305899 Reorder the terms: -13.5 + x = -10.062305899 Solving -13.5 + x = -10.062305899 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.5' to each side of the equation. -13.5 + 13.5 + x = -10.062305899 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + x = -10.062305899 + 13.5 x = -10.062305899 + 13.5 Combine like terms: -10.062305899 + 13.5 = 3.437694101 x = 3.437694101 Simplifying x = 3.437694101Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.562305899, 3.437694101}
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