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Simplifying 12x2 + -6x + -11 = 0 Reorder the terms: -11 + -6x + 12x2 = 0 Solving -11 + -6x + 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'. -0.9166666667 + -0.5x + x2 = 0 Move the constant term to the right: Add '0.9166666667' to each side of the equation. -0.9166666667 + -0.5x + 0.9166666667 + x2 = 0 + 0.9166666667 Reorder the terms: -0.9166666667 + 0.9166666667 + -0.5x + x2 = 0 + 0.9166666667 Combine like terms: -0.9166666667 + 0.9166666667 = 0.0000000000 0.0000000000 + -0.5x + x2 = 0 + 0.9166666667 -0.5x + x2 = 0 + 0.9166666667 Combine like terms: 0 + 0.9166666667 = 0.9166666667 -0.5x + x2 = 0.9166666667 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 0.9166666667 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 0.9166666667 + 0.0625 Combine like terms: 0.9166666667 + 0.0625 = 0.9791666667 0.0625 + -0.5x + x2 = 0.9791666667 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 0.9791666667 Calculate the square root of the right side: 0.989528507 Break this problem into two subproblems by setting (x + -0.25) equal to 0.989528507 and -0.989528507.Subproblem 1
x + -0.25 = 0.989528507 Simplifying x + -0.25 = 0.989528507 Reorder the terms: -0.25 + x = 0.989528507 Solving -0.25 + x = 0.989528507 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 0.989528507 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 0.989528507 + 0.25 x = 0.989528507 + 0.25 Combine like terms: 0.989528507 + 0.25 = 1.239528507 x = 1.239528507 Simplifying x = 1.239528507Subproblem 2
x + -0.25 = -0.989528507 Simplifying x + -0.25 = -0.989528507 Reorder the terms: -0.25 + x = -0.989528507 Solving -0.25 + x = -0.989528507 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -0.989528507 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -0.989528507 + 0.25 x = -0.989528507 + 0.25 Combine like terms: -0.989528507 + 0.25 = -0.739528507 x = -0.739528507 Simplifying x = -0.739528507Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.239528507, -0.739528507}
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