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Simplifying x2 + -18x + -27 = 0 Reorder the terms: -27 + -18x + x2 = 0 Solving -27 + -18x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '27' to each side of the equation. -27 + -18x + 27 + x2 = 0 + 27 Reorder the terms: -27 + 27 + -18x + x2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + -18x + x2 = 0 + 27 -18x + x2 = 0 + 27 Combine like terms: 0 + 27 = 27 -18x + x2 = 27 The x term is -18x. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18x + 81 + x2 = 27 + 81 Reorder the terms: 81 + -18x + x2 = 27 + 81 Combine like terms: 27 + 81 = 108 81 + -18x + x2 = 108 Factor a perfect square on the left side: (x + -9)(x + -9) = 108 Calculate the square root of the right side: 10.392304845 Break this problem into two subproblems by setting (x + -9) equal to 10.392304845 and -10.392304845.Subproblem 1
x + -9 = 10.392304845 Simplifying x + -9 = 10.392304845 Reorder the terms: -9 + x = 10.392304845 Solving -9 + x = 10.392304845 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 10.392304845 + 9 Combine like terms: -9 + 9 = 0 0 + x = 10.392304845 + 9 x = 10.392304845 + 9 Combine like terms: 10.392304845 + 9 = 19.392304845 x = 19.392304845 Simplifying x = 19.392304845Subproblem 2
x + -9 = -10.392304845 Simplifying x + -9 = -10.392304845 Reorder the terms: -9 + x = -10.392304845 Solving -9 + x = -10.392304845 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = -10.392304845 + 9 Combine like terms: -9 + 9 = 0 0 + x = -10.392304845 + 9 x = -10.392304845 + 9 Combine like terms: -10.392304845 + 9 = -1.392304845 x = -1.392304845 Simplifying x = -1.392304845Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.392304845, -1.392304845}
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