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Simplifying 12x2 + 5x + -11 = 0 Reorder the terms: -11 + 5x + 12x2 = 0 Solving -11 + 5x + 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 + 0.4166666667x + x2 = 0 Move the constant term to the right: Add '0.9166666667' to each side of the equation. -0.9166666667 + 0.4166666667x + 0.9166666667 + x2 = 0 + 0.9166666667 Reorder the terms: -0.9166666667 + 0.9166666667 + 0.4166666667x + x2 = 0 + 0.9166666667 Combine like terms: -0.9166666667 + 0.9166666667 = 0.0000000000 0.0000000000 + 0.4166666667x + x2 = 0 + 0.9166666667 0.4166666667x + x2 = 0 + 0.9166666667 Combine like terms: 0 + 0.9166666667 = 0.9166666667 0.4166666667x + x2 = 0.9166666667 The x term is 0.4166666667x. Take half its coefficient (0.2083333334). Square it (0.04340277781) and add it to both sides. Add '0.04340277781' to each side of the equation. 0.4166666667x + 0.04340277781 + x2 = 0.9166666667 + 0.04340277781 Reorder the terms: 0.04340277781 + 0.4166666667x + x2 = 0.9166666667 + 0.04340277781 Combine like terms: 0.9166666667 + 0.04340277781 = 0.96006944451 0.04340277781 + 0.4166666667x + x2 = 0.96006944451 Factor a perfect square on the left side: (x + 0.2083333334)(x + 0.2083333334) = 0.96006944451 Calculate the square root of the right side: 0.979831335 Break this problem into two subproblems by setting (x + 0.2083333334) equal to 0.979831335 and -0.979831335.Subproblem 1
x + 0.2083333334 = 0.979831335 Simplifying x + 0.2083333334 = 0.979831335 Reorder the terms: 0.2083333334 + x = 0.979831335 Solving 0.2083333334 + x = 0.979831335 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2083333334' to each side of the equation. 0.2083333334 + -0.2083333334 + x = 0.979831335 + -0.2083333334 Combine like terms: 0.2083333334 + -0.2083333334 = 0.0000000000 0.0000000000 + x = 0.979831335 + -0.2083333334 x = 0.979831335 + -0.2083333334 Combine like terms: 0.979831335 + -0.2083333334 = 0.7714980016 x = 0.7714980016 Simplifying x = 0.7714980016Subproblem 2
x + 0.2083333334 = -0.979831335 Simplifying x + 0.2083333334 = -0.979831335 Reorder the terms: 0.2083333334 + x = -0.979831335 Solving 0.2083333334 + x = -0.979831335 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2083333334' to each side of the equation. 0.2083333334 + -0.2083333334 + x = -0.979831335 + -0.2083333334 Combine like terms: 0.2083333334 + -0.2083333334 = 0.0000000000 0.0000000000 + x = -0.979831335 + -0.2083333334 x = -0.979831335 + -0.2083333334 Combine like terms: -0.979831335 + -0.2083333334 = -1.1881646684 x = -1.1881646684 Simplifying x = -1.1881646684Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7714980016, -1.1881646684}
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