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Simplifying 2(1 + -2x)(x + 3) + -1(2 + -1x) * 5x = 0 Reorder the terms: 2(1 + -2x)(3 + x) + -1(2 + -1x) * 5x = 0 Multiply (1 + -2x) * (3 + x) 2(1(3 + x) + -2x * (3 + x)) + -1(2 + -1x) * 5x = 0 2((3 * 1 + x * 1) + -2x * (3 + x)) + -1(2 + -1x) * 5x = 0 2((3 + 1x) + -2x * (3 + x)) + -1(2 + -1x) * 5x = 0 2(3 + 1x + (3 * -2x + x * -2x)) + -1(2 + -1x) * 5x = 0 2(3 + 1x + (-6x + -2x2)) + -1(2 + -1x) * 5x = 0 Combine like terms: 1x + -6x = -5x 2(3 + -5x + -2x2) + -1(2 + -1x) * 5x = 0 (3 * 2 + -5x * 2 + -2x2 * 2) + -1(2 + -1x) * 5x = 0 (6 + -10x + -4x2) + -1(2 + -1x) * 5x = 0 Reorder the terms for easier multiplication: 6 + -10x + -4x2 + -1 * 5x(2 + -1x) = 0 Multiply -1 * 5 6 + -10x + -4x2 + -5x(2 + -1x) = 0 6 + -10x + -4x2 + (2 * -5x + -1x * -5x) = 0 6 + -10x + -4x2 + (-10x + 5x2) = 0 Reorder the terms: 6 + -10x + -10x + -4x2 + 5x2 = 0 Combine like terms: -10x + -10x = -20x 6 + -20x + -4x2 + 5x2 = 0 Combine like terms: -4x2 + 5x2 = 1x2 6 + -20x + 1x2 = 0 Solving 6 + -20x + 1x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + -20x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + -20x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -20x + x2 = 0 + -6 -20x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 -20x + x2 = -6 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = -6 + 100 Reorder the terms: 100 + -20x + x2 = -6 + 100 Combine like terms: -6 + 100 = 94 100 + -20x + x2 = 94 Factor a perfect square on the left side: (x + -10)(x + -10) = 94 Calculate the square root of the right side: 9.695359715 Break this problem into two subproblems by setting (x + -10) equal to 9.695359715 and -9.695359715.Subproblem 1
x + -10 = 9.695359715 Simplifying x + -10 = 9.695359715 Reorder the terms: -10 + x = 9.695359715 Solving -10 + x = 9.695359715 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 9.695359715 + 10 Combine like terms: -10 + 10 = 0 0 + x = 9.695359715 + 10 x = 9.695359715 + 10 Combine like terms: 9.695359715 + 10 = 19.695359715 x = 19.695359715 Simplifying x = 19.695359715Subproblem 2
x + -10 = -9.695359715 Simplifying x + -10 = -9.695359715 Reorder the terms: -10 + x = -9.695359715 Solving -10 + x = -9.695359715 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -9.695359715 + 10 Combine like terms: -10 + 10 = 0 0 + x = -9.695359715 + 10 x = -9.695359715 + 10 Combine like terms: -9.695359715 + 10 = 0.304640285 x = 0.304640285 Simplifying x = 0.304640285Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.695359715, 0.304640285}
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