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Simplifying (2x3 + -3x2 + x) + -1(2x3 + 8x2 + -1) = 0 Reorder the terms: (x + -3x2 + 2x3) + -1(2x3 + 8x2 + -1) = 0 Remove parenthesis around (x + -3x2 + 2x3) x + -3x2 + 2x3 + -1(2x3 + 8x2 + -1) = 0 Reorder the terms: x + -3x2 + 2x3 + -1(-1 + 8x2 + 2x3) = 0 x + -3x2 + 2x3 + (-1 * -1 + 8x2 * -1 + 2x3 * -1) = 0 x + -3x2 + 2x3 + (1 + -8x2 + -2x3) = 0 Reorder the terms: 1 + x + -3x2 + -8x2 + 2x3 + -2x3 = 0 Combine like terms: -3x2 + -8x2 = -11x2 1 + x + -11x2 + 2x3 + -2x3 = 0 Combine like terms: 2x3 + -2x3 = 0 1 + x + -11x2 + 0 = 0 1 + x + -11x2 = 0 Solving 1 + x + -11x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -11 the coefficient of the squared term: Divide each side by '-11'. -0.09090909091 + -0.09090909091x + x2 = 0 Move the constant term to the right: Add '0.09090909091' to each side of the equation. -0.09090909091 + -0.09090909091x + 0.09090909091 + x2 = 0 + 0.09090909091 Reorder the terms: -0.09090909091 + 0.09090909091 + -0.09090909091x + x2 = 0 + 0.09090909091 Combine like terms: -0.09090909091 + 0.09090909091 = 0.00000000000 0.00000000000 + -0.09090909091x + x2 = 0 + 0.09090909091 -0.09090909091x + x2 = 0 + 0.09090909091 Combine like terms: 0 + 0.09090909091 = 0.09090909091 -0.09090909091x + x2 = 0.09090909091 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -0.09090909091x + 0.25 + x2 = 0.09090909091 + 0.25 Reorder the terms: 0.25 + -0.09090909091x + x2 = 0.09090909091 + 0.25 Combine like terms: 0.09090909091 + 0.25 = 0.34090909091 0.25 + -0.09090909091x + x2 = 0.34090909091 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.34090909091 Calculate the square root of the right side: 0.583874208 Break this problem into two subproblems by setting (x + 0.5) equal to 0.583874208 and -0.583874208.Subproblem 1
x + 0.5 = 0.583874208 Simplifying x + 0.5 = 0.583874208 Reorder the terms: 0.5 + x = 0.583874208 Solving 0.5 + x = 0.583874208 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 0.583874208 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.583874208 + -0.5 x = 0.583874208 + -0.5 Combine like terms: 0.583874208 + -0.5 = 0.083874208 x = 0.083874208 Simplifying x = 0.083874208Subproblem 2
x + 0.5 = -0.583874208 Simplifying x + 0.5 = -0.583874208 Reorder the terms: 0.5 + x = -0.583874208 Solving 0.5 + x = -0.583874208 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -0.583874208 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.583874208 + -0.5 x = -0.583874208 + -0.5 Combine like terms: -0.583874208 + -0.5 = -1.083874208 x = -1.083874208 Simplifying x = -1.083874208Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.083874208, -1.083874208}
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