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Simplifying 2x2 + -3x2 + -18x + 27 = 0 Reorder the terms: 27 + -18x + 2x2 + -3x2 = 0 Combine like terms: 2x2 + -3x2 = -1x2 27 + -18x + -1x2 = 0 Solving 27 + -18x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -27 + 18x + x2 = 0 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 = 1.392304845 x = 1.392304845 Simplifying x = 1.392304845Subproblem 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 = -19.392304845 x = -19.392304845 Simplifying x = -19.392304845Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.392304845, -19.392304845}
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