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Simplifying 0 = 12x2 + 11x + -6 Reorder the terms: 0 = -6 + 11x + 12x2 Solving 0 = -6 + 11x + 12x2 Solving for variable 'x'. Combine like terms: 0 + 6 = 6 6 + -11x + -12x2 = -6 + 11x + 12x2 + 6 + -11x + -12x2 Reorder the terms: 6 + -11x + -12x2 = -6 + 6 + 11x + -11x + 12x2 + -12x2 Combine like terms: -6 + 6 = 0 6 + -11x + -12x2 = 0 + 11x + -11x + 12x2 + -12x2 6 + -11x + -12x2 = 11x + -11x + 12x2 + -12x2 Combine like terms: 11x + -11x = 0 6 + -11x + -12x2 = 0 + 12x2 + -12x2 6 + -11x + -12x2 = 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 6 + -11x + -12x2 = 0 Begin completing the square. Divide all terms by -12 the coefficient of the squared term: Divide each side by '-12'. -0.5 + 0.9166666667x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 0.9166666667x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 0.9166666667x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 0.9166666667x + x2 = 0 + 0.5 0.9166666667x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 0.9166666667x + x2 = 0.5 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 = 0.5 + 0.2100694445 Reorder the terms: 0.2100694445 + 0.9166666667x + x2 = 0.5 + 0.2100694445 Combine like terms: 0.5 + 0.2100694445 = 0.7100694445 0.2100694445 + 0.9166666667x + x2 = 0.7100694445 Factor a perfect square on the left side: (x + 0.4583333334)(x + 0.4583333334) = 0.7100694445 Calculate the square root of the right side: 0.842656184 Break this problem into two subproblems by setting (x + 0.4583333334) equal to 0.842656184 and -0.842656184.Subproblem 1
x + 0.4583333334 = 0.842656184 Simplifying x + 0.4583333334 = 0.842656184 Reorder the terms: 0.4583333334 + x = 0.842656184 Solving 0.4583333334 + x = 0.842656184 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 = 0.842656184 + -0.4583333334 Combine like terms: 0.4583333334 + -0.4583333334 = 0.0000000000 0.0000000000 + x = 0.842656184 + -0.4583333334 x = 0.842656184 + -0.4583333334 Combine like terms: 0.842656184 + -0.4583333334 = 0.3843228506 x = 0.3843228506 Simplifying x = 0.3843228506Subproblem 2
x + 0.4583333334 = -0.842656184 Simplifying x + 0.4583333334 = -0.842656184 Reorder the terms: 0.4583333334 + x = -0.842656184 Solving 0.4583333334 + x = -0.842656184 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 = -0.842656184 + -0.4583333334 Combine like terms: 0.4583333334 + -0.4583333334 = 0.0000000000 0.0000000000 + x = -0.842656184 + -0.4583333334 x = -0.842656184 + -0.4583333334 Combine like terms: -0.842656184 + -0.4583333334 = -1.3009895174 x = -1.3009895174 Simplifying x = -1.3009895174Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3843228506, -1.3009895174}
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