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Simplifying 3x2 + -5.6x + -12 = 0 Reorder the terms: -12 + -5.6x + 3x2 = 0 Solving -12 + -5.6x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -4 + -1.866666667x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -1.866666667x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -1.866666667x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1.866666667x + x2 = 0 + 4 -1.866666667x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -1.866666667x + x2 = 4 The x term is -1.866666667x. Take half its coefficient (-0.9333333335). Square it (0.8711111114) and add it to both sides. Add '0.8711111114' to each side of the equation. -1.866666667x + 0.8711111114 + x2 = 4 + 0.8711111114 Reorder the terms: 0.8711111114 + -1.866666667x + x2 = 4 + 0.8711111114 Combine like terms: 4 + 0.8711111114 = 4.8711111114 0.8711111114 + -1.866666667x + x2 = 4.8711111114 Factor a perfect square on the left side: (x + -0.9333333335)(x + -0.9333333335) = 4.8711111114 Calculate the square root of the right side: 2.207059381 Break this problem into two subproblems by setting (x + -0.9333333335) equal to 2.207059381 and -2.207059381.Subproblem 1
x + -0.9333333335 = 2.207059381 Simplifying x + -0.9333333335 = 2.207059381 Reorder the terms: -0.9333333335 + x = 2.207059381 Solving -0.9333333335 + x = 2.207059381 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9333333335' to each side of the equation. -0.9333333335 + 0.9333333335 + x = 2.207059381 + 0.9333333335 Combine like terms: -0.9333333335 + 0.9333333335 = 0.0000000000 0.0000000000 + x = 2.207059381 + 0.9333333335 x = 2.207059381 + 0.9333333335 Combine like terms: 2.207059381 + 0.9333333335 = 3.1403927145 x = 3.1403927145 Simplifying x = 3.1403927145Subproblem 2
x + -0.9333333335 = -2.207059381 Simplifying x + -0.9333333335 = -2.207059381 Reorder the terms: -0.9333333335 + x = -2.207059381 Solving -0.9333333335 + x = -2.207059381 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9333333335' to each side of the equation. -0.9333333335 + 0.9333333335 + x = -2.207059381 + 0.9333333335 Combine like terms: -0.9333333335 + 0.9333333335 = 0.0000000000 0.0000000000 + x = -2.207059381 + 0.9333333335 x = -2.207059381 + 0.9333333335 Combine like terms: -2.207059381 + 0.9333333335 = -1.2737260475 x = -1.2737260475 Simplifying x = -1.2737260475Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.1403927145, -1.2737260475}
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