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Simplifying 12x2 + 11x + -4 = 0 Reorder the terms: -4 + 11x + 12x2 = 0 Solving -4 + 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'. -0.3333333333 + 0.9166666667x + x2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + 0.9166666667x + 0.3333333333 + x2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + 0.9166666667x + x2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + 0.9166666667x + x2 = 0 + 0.3333333333 0.9166666667x + x2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 0.9166666667x + x2 = 0.3333333333 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 = 0.3333333333 + 0.2100694445 Reorder the terms: 0.2100694445 + 0.9166666667x + x2 = 0.3333333333 + 0.2100694445 Combine like terms: 0.3333333333 + 0.2100694445 = 0.5434027778 0.2100694445 + 0.9166666667x + x2 = 0.5434027778 Factor a perfect square on the left side: (x + 0.4583333334)(x + 0.4583333334) = 0.5434027778 Calculate the square root of the right side: 0.737158584 Break this problem into two subproblems by setting (x + 0.4583333334) equal to 0.737158584 and -0.737158584.Subproblem 1
x + 0.4583333334 = 0.737158584 Simplifying x + 0.4583333334 = 0.737158584 Reorder the terms: 0.4583333334 + x = 0.737158584 Solving 0.4583333334 + x = 0.737158584 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 = 0.737158584 + -0.4583333334 Combine like terms: 0.4583333334 + -0.4583333334 = 0.0000000000 0.0000000000 + x = 0.737158584 + -0.4583333334 x = 0.737158584 + -0.4583333334 Combine like terms: 0.737158584 + -0.4583333334 = 0.2788252506 x = 0.2788252506 Simplifying x = 0.2788252506Subproblem 2
x + 0.4583333334 = -0.737158584 Simplifying x + 0.4583333334 = -0.737158584 Reorder the terms: 0.4583333334 + x = -0.737158584 Solving 0.4583333334 + x = -0.737158584 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 = -0.737158584 + -0.4583333334 Combine like terms: 0.4583333334 + -0.4583333334 = 0.0000000000 0.0000000000 + x = -0.737158584 + -0.4583333334 x = -0.737158584 + -0.4583333334 Combine like terms: -0.737158584 + -0.4583333334 = -1.1954919174 x = -1.1954919174 Simplifying x = -1.1954919174Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2788252506, -1.1954919174}
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