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Simplifying 12x2 + 44x + -5 = 0 Reorder the terms: -5 + 44x + 12x2 = 0 Solving -5 + 44x + 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'. -0.4166666667 + 3.666666667x + x2 = 0 Move the constant term to the right: Add '0.4166666667' to each side of the equation. -0.4166666667 + 3.666666667x + 0.4166666667 + x2 = 0 + 0.4166666667 Reorder the terms: -0.4166666667 + 0.4166666667 + 3.666666667x + x2 = 0 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + 3.666666667x + x2 = 0 + 0.4166666667 3.666666667x + x2 = 0 + 0.4166666667 Combine like terms: 0 + 0.4166666667 = 0.4166666667 3.666666667x + x2 = 0.4166666667 The x term is 3.666666667x. Take half its coefficient (1.833333334). Square it (3.361111114) and add it to both sides. Add '3.361111114' to each side of the equation. 3.666666667x + 3.361111114 + x2 = 0.4166666667 + 3.361111114 Reorder the terms: 3.361111114 + 3.666666667x + x2 = 0.4166666667 + 3.361111114 Combine like terms: 0.4166666667 + 3.361111114 = 3.7777777807 3.361111114 + 3.666666667x + x2 = 3.7777777807 Factor a perfect square on the left side: (x + 1.833333334)(x + 1.833333334) = 3.7777777807 Calculate the square root of the right side: 1.943650632 Break this problem into two subproblems by setting (x + 1.833333334) equal to 1.943650632 and -1.943650632.Subproblem 1
x + 1.833333334 = 1.943650632 Simplifying x + 1.833333334 = 1.943650632 Reorder the terms: 1.833333334 + x = 1.943650632 Solving 1.833333334 + x = 1.943650632 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.833333334' to each side of the equation. 1.833333334 + -1.833333334 + x = 1.943650632 + -1.833333334 Combine like terms: 1.833333334 + -1.833333334 = 0.000000000 0.000000000 + x = 1.943650632 + -1.833333334 x = 1.943650632 + -1.833333334 Combine like terms: 1.943650632 + -1.833333334 = 0.110317298 x = 0.110317298 Simplifying x = 0.110317298Subproblem 2
x + 1.833333334 = -1.943650632 Simplifying x + 1.833333334 = -1.943650632 Reorder the terms: 1.833333334 + x = -1.943650632 Solving 1.833333334 + x = -1.943650632 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.833333334' to each side of the equation. 1.833333334 + -1.833333334 + x = -1.943650632 + -1.833333334 Combine like terms: 1.833333334 + -1.833333334 = 0.000000000 0.000000000 + x = -1.943650632 + -1.833333334 x = -1.943650632 + -1.833333334 Combine like terms: -1.943650632 + -1.833333334 = -3.776983966 x = -3.776983966 Simplifying x = -3.776983966Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.110317298, -3.776983966}
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