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Simplifying 2x2 + -12x + -27 = 0 Reorder the terms: -27 + -12x + 2x2 = 0 Solving -27 + -12x + 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 + -6x + x2 = 0 Move the constant term to the right: Add '13.5' to each side of the equation. -13.5 + -6x + 13.5 + x2 = 0 + 13.5 Reorder the terms: -13.5 + 13.5 + -6x + x2 = 0 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + -6x + x2 = 0 + 13.5 -6x + x2 = 0 + 13.5 Combine like terms: 0 + 13.5 = 13.5 -6x + x2 = 13.5 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 13.5 + 9 Reorder the terms: 9 + -6x + x2 = 13.5 + 9 Combine like terms: 13.5 + 9 = 22.5 9 + -6x + x2 = 22.5 Factor a perfect square on the left side: (x + -3)(x + -3) = 22.5 Calculate the square root of the right side: 4.74341649 Break this problem into two subproblems by setting (x + -3) equal to 4.74341649 and -4.74341649.Subproblem 1
x + -3 = 4.74341649 Simplifying x + -3 = 4.74341649 Reorder the terms: -3 + x = 4.74341649 Solving -3 + x = 4.74341649 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 4.74341649 + 3 Combine like terms: -3 + 3 = 0 0 + x = 4.74341649 + 3 x = 4.74341649 + 3 Combine like terms: 4.74341649 + 3 = 7.74341649 x = 7.74341649 Simplifying x = 7.74341649Subproblem 2
x + -3 = -4.74341649 Simplifying x + -3 = -4.74341649 Reorder the terms: -3 + x = -4.74341649 Solving -3 + x = -4.74341649 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -4.74341649 + 3 Combine like terms: -3 + 3 = 0 0 + x = -4.74341649 + 3 x = -4.74341649 + 3 Combine like terms: -4.74341649 + 3 = -1.74341649 x = -1.74341649 Simplifying x = -1.74341649Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.74341649, -1.74341649}
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