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Simplifying 16x[3x + -1(6 + -9x)] = 30x + [-1(3x + 2) + -1(x + 3)] 16x[3x + (6 * -1 + -9x * -1)] = 30x + [-1(3x + 2) + -1(x + 3)] 16x[3x + (-6 + 9x)] = 30x + [-1(3x + 2) + -1(x + 3)] Reorder the terms: 16x[-6 + 3x + 9x] = 30x + [-1(3x + 2) + -1(x + 3)] Combine like terms: 3x + 9x = 12x 16x[-6 + 12x] = 30x + [-1(3x + 2) + -1(x + 3)] [-6 * 16x + 12x * 16x] = 30x + [-1(3x + 2) + -1(x + 3)] [-96x + 192x2] = 30x + [-1(3x + 2) + -1(x + 3)] Reorder the terms: -96x + 192x2 = 30x + [-1(2 + 3x) + -1(x + 3)] -96x + 192x2 = 30x + [(2 * -1 + 3x * -1) + -1(x + 3)] -96x + 192x2 = 30x + [(-2 + -3x) + -1(x + 3)] Reorder the terms: -96x + 192x2 = 30x + [-2 + -3x + -1(3 + x)] -96x + 192x2 = 30x + [-2 + -3x + (3 * -1 + x * -1)] -96x + 192x2 = 30x + [-2 + -3x + (-3 + -1x)] Reorder the terms: -96x + 192x2 = 30x + [-2 + -3 + -3x + -1x] Combine like terms: -2 + -3 = -5 -96x + 192x2 = 30x + [-5 + -3x + -1x] Combine like terms: -3x + -1x = -4x -96x + 192x2 = 30x + [-5 + -4x] Remove brackets around [-5 + -4x] -96x + 192x2 = 30x + -5 + -4x Reorder the terms: -96x + 192x2 = -5 + 30x + -4x Combine like terms: 30x + -4x = 26x -96x + 192x2 = -5 + 26x Solving -96x + 192x2 = -5 + 26x Solving for variable 'x'. Reorder the terms: 5 + -96x + -26x + 192x2 = -5 + 26x + 5 + -26x Combine like terms: -96x + -26x = -122x 5 + -122x + 192x2 = -5 + 26x + 5 + -26x Reorder the terms: 5 + -122x + 192x2 = -5 + 5 + 26x + -26x Combine like terms: -5 + 5 = 0 5 + -122x + 192x2 = 0 + 26x + -26x 5 + -122x + 192x2 = 26x + -26x Combine like terms: 26x + -26x = 0 5 + -122x + 192x2 = 0 Begin completing the square. Divide all terms by 192 the coefficient of the squared term: Divide each side by '192'. 0.02604166667 + -0.6354166667x + x2 = 0 Move the constant term to the right: Add '-0.02604166667' to each side of the equation. 0.02604166667 + -0.6354166667x + -0.02604166667 + x2 = 0 + -0.02604166667 Reorder the terms: 0.02604166667 + -0.02604166667 + -0.6354166667x + x2 = 0 + -0.02604166667 Combine like terms: 0.02604166667 + -0.02604166667 = 0.00000000000 0.00000000000 + -0.6354166667x + x2 = 0 + -0.02604166667 -0.6354166667x + x2 = 0 + -0.02604166667 Combine like terms: 0 + -0.02604166667 = -0.02604166667 -0.6354166667x + x2 = -0.02604166667 The x term is -0.6354166667x. Take half its coefficient (-0.3177083334). Square it (0.1009385851) and add it to both sides. Add '0.1009385851' to each side of the equation. -0.6354166667x + 0.1009385851 + x2 = -0.02604166667 + 0.1009385851 Reorder the terms: 0.1009385851 + -0.6354166667x + x2 = -0.02604166667 + 0.1009385851 Combine like terms: -0.02604166667 + 0.1009385851 = 0.07489691843 0.1009385851 + -0.6354166667x + x2 = 0.07489691843 Factor a perfect square on the left side: (x + -0.3177083334)(x + -0.3177083334) = 0.07489691843 Calculate the square root of the right side: 0.273673014 Break this problem into two subproblems by setting (x + -0.3177083334) equal to 0.273673014 and -0.273673014.Subproblem 1
x + -0.3177083334 = 0.273673014 Simplifying x + -0.3177083334 = 0.273673014 Reorder the terms: -0.3177083334 + x = 0.273673014 Solving -0.3177083334 + x = 0.273673014 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3177083334' to each side of the equation. -0.3177083334 + 0.3177083334 + x = 0.273673014 + 0.3177083334 Combine like terms: -0.3177083334 + 0.3177083334 = 0.0000000000 0.0000000000 + x = 0.273673014 + 0.3177083334 x = 0.273673014 + 0.3177083334 Combine like terms: 0.273673014 + 0.3177083334 = 0.5913813474 x = 0.5913813474 Simplifying x = 0.5913813474Subproblem 2
x + -0.3177083334 = -0.273673014 Simplifying x + -0.3177083334 = -0.273673014 Reorder the terms: -0.3177083334 + x = -0.273673014 Solving -0.3177083334 + x = -0.273673014 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3177083334' to each side of the equation. -0.3177083334 + 0.3177083334 + x = -0.273673014 + 0.3177083334 Combine like terms: -0.3177083334 + 0.3177083334 = 0.0000000000 0.0000000000 + x = -0.273673014 + 0.3177083334 x = -0.273673014 + 0.3177083334 Combine like terms: -0.273673014 + 0.3177083334 = 0.0440353194 x = 0.0440353194 Simplifying x = 0.0440353194Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5913813474, 0.0440353194}
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