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Simplifying 12x2 + 22x + -8 = 0 Reorder the terms: -8 + 22x + 12x2 = 0 Solving -8 + 22x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + 11x + 6x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + 11x + 6x2)' equal to zero and attempt to solve: Simplifying -4 + 11x + 6x2 = 0 Solving -4 + 11x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.6666666667 + 1.833333333x + x2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + 1.833333333x + 0.6666666667 + x2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + 1.833333333x + x2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + 1.833333333x + x2 = 0 + 0.6666666667 1.833333333x + x2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 1.833333333x + x2 = 0.6666666667 The x term is 1.833333333x. Take half its coefficient (0.9166666665). Square it (0.8402777775) and add it to both sides. Add '0.8402777775' to each side of the equation. 1.833333333x + 0.8402777775 + x2 = 0.6666666667 + 0.8402777775 Reorder the terms: 0.8402777775 + 1.833333333x + x2 = 0.6666666667 + 0.8402777775 Combine like terms: 0.6666666667 + 0.8402777775 = 1.5069444442 0.8402777775 + 1.833333333x + x2 = 1.5069444442 Factor a perfect square on the left side: (x + 0.9166666665)(x + 0.9166666665) = 1.5069444442 Calculate the square root of the right side: 1.227576655 Break this problem into two subproblems by setting (x + 0.9166666665) equal to 1.227576655 and -1.227576655.Subproblem 1
x + 0.9166666665 = 1.227576655 Simplifying x + 0.9166666665 = 1.227576655 Reorder the terms: 0.9166666665 + x = 1.227576655 Solving 0.9166666665 + x = 1.227576655 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9166666665' to each side of the equation. 0.9166666665 + -0.9166666665 + x = 1.227576655 + -0.9166666665 Combine like terms: 0.9166666665 + -0.9166666665 = 0.0000000000 0.0000000000 + x = 1.227576655 + -0.9166666665 x = 1.227576655 + -0.9166666665 Combine like terms: 1.227576655 + -0.9166666665 = 0.3109099885 x = 0.3109099885 Simplifying x = 0.3109099885Subproblem 2
x + 0.9166666665 = -1.227576655 Simplifying x + 0.9166666665 = -1.227576655 Reorder the terms: 0.9166666665 + x = -1.227576655 Solving 0.9166666665 + x = -1.227576655 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9166666665' to each side of the equation. 0.9166666665 + -0.9166666665 + x = -1.227576655 + -0.9166666665 Combine like terms: 0.9166666665 + -0.9166666665 = 0.0000000000 0.0000000000 + x = -1.227576655 + -0.9166666665 x = -1.227576655 + -0.9166666665 Combine like terms: -1.227576655 + -0.9166666665 = -2.1442433215 x = -2.1442433215 Simplifying x = -2.1442433215Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3109099885, -2.1442433215}Solution
x = {0.3109099885, -2.1442433215}
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