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Simplifying 3x2 + 16x + 9 = -16x + -12 Reorder the terms: 9 + 16x + 3x2 = -16x + -12 Reorder the terms: 9 + 16x + 3x2 = -12 + -16x Solving 9 + 16x + 3x2 = -12 + -16x Solving for variable 'x'. Reorder the terms: 9 + 12 + 16x + 16x + 3x2 = -12 + -16x + 12 + 16x Combine like terms: 9 + 12 = 21 21 + 16x + 16x + 3x2 = -12 + -16x + 12 + 16x Combine like terms: 16x + 16x = 32x 21 + 32x + 3x2 = -12 + -16x + 12 + 16x Reorder the terms: 21 + 32x + 3x2 = -12 + 12 + -16x + 16x Combine like terms: -12 + 12 = 0 21 + 32x + 3x2 = 0 + -16x + 16x 21 + 32x + 3x2 = -16x + 16x Combine like terms: -16x + 16x = 0 21 + 32x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 7 + 10.66666667x + x2 = 0 Move the constant term to the right: Add '-7' to each side of the equation. 7 + 10.66666667x + -7 + x2 = 0 + -7 Reorder the terms: 7 + -7 + 10.66666667x + x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 10.66666667x + x2 = 0 + -7 10.66666667x + x2 = 0 + -7 Combine like terms: 0 + -7 = -7 10.66666667x + x2 = -7 The x term is 10.66666667x. Take half its coefficient (5.333333335). Square it (28.44444446) and add it to both sides. Add '28.44444446' to each side of the equation. 10.66666667x + 28.44444446 + x2 = -7 + 28.44444446 Reorder the terms: 28.44444446 + 10.66666667x + x2 = -7 + 28.44444446 Combine like terms: -7 + 28.44444446 = 21.44444446 28.44444446 + 10.66666667x + x2 = 21.44444446 Factor a perfect square on the left side: (x + 5.333333335)(x + 5.333333335) = 21.44444446 Calculate the square root of the right side: 4.630814665 Break this problem into two subproblems by setting (x + 5.333333335) equal to 4.630814665 and -4.630814665.Subproblem 1
x + 5.333333335 = 4.630814665 Simplifying x + 5.333333335 = 4.630814665 Reorder the terms: 5.333333335 + x = 4.630814665 Solving 5.333333335 + x = 4.630814665 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.333333335' to each side of the equation. 5.333333335 + -5.333333335 + x = 4.630814665 + -5.333333335 Combine like terms: 5.333333335 + -5.333333335 = 0.000000000 0.000000000 + x = 4.630814665 + -5.333333335 x = 4.630814665 + -5.333333335 Combine like terms: 4.630814665 + -5.333333335 = -0.70251867 x = -0.70251867 Simplifying x = -0.70251867Subproblem 2
x + 5.333333335 = -4.630814665 Simplifying x + 5.333333335 = -4.630814665 Reorder the terms: 5.333333335 + x = -4.630814665 Solving 5.333333335 + x = -4.630814665 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.333333335' to each side of the equation. 5.333333335 + -5.333333335 + x = -4.630814665 + -5.333333335 Combine like terms: 5.333333335 + -5.333333335 = 0.000000000 0.000000000 + x = -4.630814665 + -5.333333335 x = -4.630814665 + -5.333333335 Combine like terms: -4.630814665 + -5.333333335 = -9.964148 x = -9.964148 Simplifying x = -9.964148Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.70251867, -9.964148}
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