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Simplifying 12x2 + 11x + -27 = 0 Reorder the terms: -27 + 11x + 12x2 = 0 Solving -27 + 11x + 12x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -2.25 + 0.9166666667x + x2 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + 0.9166666667x + 2.25 + x2 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + 0.9166666667x + x2 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + 0.9166666667x + x2 = 0 + 2.25 0.9166666667x + x2 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 0.9166666667x + x2 = 2.25 The x term is 0.9166666667x. Take half its coefficient (0.4583333334). Square it (0.2100694445) and add it to both sides. Add '0.2100694445' to each side of the equation. 0.9166666667x + 0.2100694445 + x2 = 2.25 + 0.2100694445 Reorder the terms: 0.2100694445 + 0.9166666667x + x2 = 2.25 + 0.2100694445 Combine like terms: 2.25 + 0.2100694445 = 2.4600694445 0.2100694445 + 0.9166666667x + x2 = 2.4600694445 Factor a perfect square on the left side: (x + 0.4583333334)(x + 0.4583333334) = 2.4600694445 Calculate the square root of the right side: 1.568460852 Break this problem into two subproblems by setting (x + 0.4583333334) equal to 1.568460852 and -1.568460852.Subproblem 1
x + 0.4583333334 = 1.568460852 Simplifying x + 0.4583333334 = 1.568460852 Reorder the terms: 0.4583333334 + x = 1.568460852 Solving 0.4583333334 + x = 1.568460852 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4583333334' to each side of the equation. 0.4583333334 + -0.4583333334 + x = 1.568460852 + -0.4583333334 Combine like terms: 0.4583333334 + -0.4583333334 = 0.0000000000 0.0000000000 + x = 1.568460852 + -0.4583333334 x = 1.568460852 + -0.4583333334 Combine like terms: 1.568460852 + -0.4583333334 = 1.1101275186 x = 1.1101275186 Simplifying x = 1.1101275186Subproblem 2
x + 0.4583333334 = -1.568460852 Simplifying x + 0.4583333334 = -1.568460852 Reorder the terms: 0.4583333334 + x = -1.568460852 Solving 0.4583333334 + x = -1.568460852 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4583333334' to each side of the equation. 0.4583333334 + -0.4583333334 + x = -1.568460852 + -0.4583333334 Combine like terms: 0.4583333334 + -0.4583333334 = 0.0000000000 0.0000000000 + x = -1.568460852 + -0.4583333334 x = -1.568460852 + -0.4583333334 Combine like terms: -1.568460852 + -0.4583333334 = -2.0267941854 x = -2.0267941854 Simplifying x = -2.0267941854Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1101275186, -2.0267941854}
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