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Simplifying 2x2 + -6x + -27 = 0 Reorder the terms: -27 + -6x + 2x2 = 0 Solving -27 + -6x + 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 + -3x + x2 = 0 Move the constant term to the right: Add '13.5' to each side of the equation. -13.5 + -3x + 13.5 + x2 = 0 + 13.5 Reorder the terms: -13.5 + 13.5 + -3x + x2 = 0 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + -3x + x2 = 0 + 13.5 -3x + x2 = 0 + 13.5 Combine like terms: 0 + 13.5 = 13.5 -3x + x2 = 13.5 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 13.5 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 13.5 + 2.25 Combine like terms: 13.5 + 2.25 = 15.75 2.25 + -3x + x2 = 15.75 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 15.75 Calculate the square root of the right side: 3.968626967 Break this problem into two subproblems by setting (x + -1.5) equal to 3.968626967 and -3.968626967.Subproblem 1
x + -1.5 = 3.968626967 Simplifying x + -1.5 = 3.968626967 Reorder the terms: -1.5 + x = 3.968626967 Solving -1.5 + x = 3.968626967 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 3.968626967 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 3.968626967 + 1.5 x = 3.968626967 + 1.5 Combine like terms: 3.968626967 + 1.5 = 5.468626967 x = 5.468626967 Simplifying x = 5.468626967Subproblem 2
x + -1.5 = -3.968626967 Simplifying x + -1.5 = -3.968626967 Reorder the terms: -1.5 + x = -3.968626967 Solving -1.5 + x = -3.968626967 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -3.968626967 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -3.968626967 + 1.5 x = -3.968626967 + 1.5 Combine like terms: -3.968626967 + 1.5 = -2.468626967 x = -2.468626967 Simplifying x = -2.468626967Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.468626967, -2.468626967}
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