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Simplifying 2x2 + 18x + 27 = 0 Reorder the terms: 27 + 18x + 2x2 = 0 Solving 27 + 18x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 13.5 + 9x + x2 = 0 Move the constant term to the right: Add '-13.5' to each side of the equation. 13.5 + 9x + -13.5 + x2 = 0 + -13.5 Reorder the terms: 13.5 + -13.5 + 9x + x2 = 0 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + 9x + x2 = 0 + -13.5 9x + x2 = 0 + -13.5 Combine like terms: 0 + -13.5 = -13.5 9x + x2 = -13.5 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = -13.5 + 20.25 Reorder the terms: 20.25 + 9x + x2 = -13.5 + 20.25 Combine like terms: -13.5 + 20.25 = 6.75 20.25 + 9x + x2 = 6.75 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 6.75 Calculate the square root of the right side: 2.598076211 Break this problem into two subproblems by setting (x + 4.5) equal to 2.598076211 and -2.598076211.Subproblem 1
x + 4.5 = 2.598076211 Simplifying x + 4.5 = 2.598076211 Reorder the terms: 4.5 + x = 2.598076211 Solving 4.5 + x = 2.598076211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 2.598076211 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 2.598076211 + -4.5 x = 2.598076211 + -4.5 Combine like terms: 2.598076211 + -4.5 = -1.901923789 x = -1.901923789 Simplifying x = -1.901923789Subproblem 2
x + 4.5 = -2.598076211 Simplifying x + 4.5 = -2.598076211 Reorder the terms: 4.5 + x = -2.598076211 Solving 4.5 + x = -2.598076211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -2.598076211 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -2.598076211 + -4.5 x = -2.598076211 + -4.5 Combine like terms: -2.598076211 + -4.5 = -7.098076211 x = -7.098076211 Simplifying x = -7.098076211Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.901923789, -7.098076211}
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