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Simplifying (x + 1) * sqrt(x + 3) + (x + 7) * sqrt(x + 10) = x2 + 6x + 1 Reorder the terms: (1 + x) * sqrt(x + 3) + (x + 7) * sqrt(x + 10) = x2 + 6x + 1 Reorder the terms: (1 + x) * qrst(3 + x) + (x + 7) * sqrt(x + 10) = x2 + 6x + 1 Reorder the terms for easier multiplication: qrst(1 + x)(3 + x) + (x + 7) * sqrt(x + 10) = x2 + 6x + 1 Multiply (1 + x) * (3 + x) qrst(1(3 + x) + x(3 + x)) + (x + 7) * sqrt(x + 10) = x2 + 6x + 1 qrst((3 * 1 + x * 1) + x(3 + x)) + (x + 7) * sqrt(x + 10) = x2 + 6x + 1 qrst((3 + 1x) + x(3 + x)) + (x + 7) * sqrt(x + 10) = x2 + 6x + 1 qrst(3 + 1x + (3 * x + x * x)) + (x + 7) * sqrt(x + 10) = x2 + 6x + 1 qrst(3 + 1x + (3x + x2)) + (x + 7) * sqrt(x + 10) = x2 + 6x + 1 Combine like terms: 1x + 3x = 4x qrst(3 + 4x + x2) + (x + 7) * sqrt(x + 10) = x2 + 6x + 1 (3 * qrst + 4x * qrst + x2 * qrst) + (x + 7) * sqrt(x + 10) = x2 + 6x + 1 (3qrst + 4qrstx + qrstx2) + (x + 7) * sqrt(x + 10) = x2 + 6x + 1 Reorder the terms: 3qrst + 4qrstx + qrstx2 + (7 + x) * sqrt(x + 10) = x2 + 6x + 1 Reorder the terms: 3qrst + 4qrstx + qrstx2 + (7 + x) * qrst(10 + x) = x2 + 6x + 1 Reorder the terms for easier multiplication: 3qrst + 4qrstx + qrstx2 + qrst(7 + x)(10 + x) = x2 + 6x + 1 Multiply (7 + x) * (10 + x) 3qrst + 4qrstx + qrstx2 + qrst(7(10 + x) + x(10 + x)) = x2 + 6x + 1 3qrst + 4qrstx + qrstx2 + qrst((10 * 7 + x * 7) + x(10 + x)) = x2 + 6x + 1 3qrst + 4qrstx + qrstx2 + qrst((70 + 7x) + x(10 + x)) = x2 + 6x + 1 3qrst + 4qrstx + qrstx2 + qrst(70 + 7x + (10 * x + x * x)) = x2 + 6x + 1 3qrst + 4qrstx + qrstx2 + qrst(70 + 7x + (10x + x2)) = x2 + 6x + 1 Combine like terms: 7x + 10x = 17x 3qrst + 4qrstx + qrstx2 + qrst(70 + 17x + x2) = x2 + 6x + 1 3qrst + 4qrstx + qrstx2 + (70 * qrst + 17x * qrst + x2 * qrst) = x2 + 6x + 1 3qrst + 4qrstx + qrstx2 + (70qrst + 17qrstx + qrstx2) = x2 + 6x + 1 Reorder the terms: 3qrst + 70qrst + 4qrstx + 17qrstx + qrstx2 + qrstx2 = x2 + 6x + 1 Combine like terms: 3qrst + 70qrst = 73qrst 73qrst + 4qrstx + 17qrstx + qrstx2 + qrstx2 = x2 + 6x + 1 Combine like terms: 4qrstx + 17qrstx = 21qrstx 73qrst + 21qrstx + qrstx2 + qrstx2 = x2 + 6x + 1 Combine like terms: qrstx2 + qrstx2 = 2qrstx2 73qrst + 21qrstx + 2qrstx2 = x2 + 6x + 1 Reorder the terms: 73qrst + 21qrstx + 2qrstx2 = 1 + 6x + x2 Solving 73qrst + 21qrstx + 2qrstx2 = 1 + 6x + x2 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Reorder the terms: -1 + 73qrst + 21qrstx + 2qrstx2 + -6x + -1x2 = 1 + 6x + x2 + -1 + -6x + -1x2 Reorder the terms: -1 + 73qrst + 21qrstx + 2qrstx2 + -6x + -1x2 = 1 + -1 + 6x + -6x + x2 + -1x2 Combine like terms: 1 + -1 = 0 -1 + 73qrst + 21qrstx + 2qrstx2 + -6x + -1x2 = 0 + 6x + -6x + x2 + -1x2 -1 + 73qrst + 21qrstx + 2qrstx2 + -6x + -1x2 = 6x + -6x + x2 + -1x2 Combine like terms: 6x + -6x = 0 -1 + 73qrst + 21qrstx + 2qrstx2 + -6x + -1x2 = 0 + x2 + -1x2 -1 + 73qrst + 21qrstx + 2qrstx2 + -6x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -1 + 73qrst + 21qrstx + 2qrstx2 + -6x + -1x2 = 0 The solution to this equation could not be determined.
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