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Simplifying (8 + 6x)(8 + 6x) + (8x + 6)(8x + 6) = (10x + 10)(10x + 10) + 8 Multiply (8 + 6x) * (8 + 6x) (8(8 + 6x) + 6x * (8 + 6x)) + (8x + 6)(8x + 6) = (10x + 10)(10x + 10) + 8 ((8 * 8 + 6x * 8) + 6x * (8 + 6x)) + (8x + 6)(8x + 6) = (10x + 10)(10x + 10) + 8 ((64 + 48x) + 6x * (8 + 6x)) + (8x + 6)(8x + 6) = (10x + 10)(10x + 10) + 8 (64 + 48x + (8 * 6x + 6x * 6x)) + (8x + 6)(8x + 6) = (10x + 10)(10x + 10) + 8 (64 + 48x + (48x + 36x2)) + (8x + 6)(8x + 6) = (10x + 10)(10x + 10) + 8 Combine like terms: 48x + 48x = 96x (64 + 96x + 36x2) + (8x + 6)(8x + 6) = (10x + 10)(10x + 10) + 8 Reorder the terms: 64 + 96x + 36x2 + (6 + 8x)(8x + 6) = (10x + 10)(10x + 10) + 8 Reorder the terms: 64 + 96x + 36x2 + (6 + 8x)(6 + 8x) = (10x + 10)(10x + 10) + 8 Multiply (6 + 8x) * (6 + 8x) 64 + 96x + 36x2 + (6(6 + 8x) + 8x * (6 + 8x)) = (10x + 10)(10x + 10) + 8 64 + 96x + 36x2 + ((6 * 6 + 8x * 6) + 8x * (6 + 8x)) = (10x + 10)(10x + 10) + 8 64 + 96x + 36x2 + ((36 + 48x) + 8x * (6 + 8x)) = (10x + 10)(10x + 10) + 8 64 + 96x + 36x2 + (36 + 48x + (6 * 8x + 8x * 8x)) = (10x + 10)(10x + 10) + 8 64 + 96x + 36x2 + (36 + 48x + (48x + 64x2)) = (10x + 10)(10x + 10) + 8 Combine like terms: 48x + 48x = 96x 64 + 96x + 36x2 + (36 + 96x + 64x2) = (10x + 10)(10x + 10) + 8 Reorder the terms: 64 + 36 + 96x + 96x + 36x2 + 64x2 = (10x + 10)(10x + 10) + 8 Combine like terms: 64 + 36 = 100 100 + 96x + 96x + 36x2 + 64x2 = (10x + 10)(10x + 10) + 8 Combine like terms: 96x + 96x = 192x 100 + 192x + 36x2 + 64x2 = (10x + 10)(10x + 10) + 8 Combine like terms: 36x2 + 64x2 = 100x2 100 + 192x + 100x2 = (10x + 10)(10x + 10) + 8 Reorder the terms: 100 + 192x + 100x2 = (10 + 10x)(10x + 10) + 8 Reorder the terms: 100 + 192x + 100x2 = (10 + 10x)(10 + 10x) + 8 Multiply (10 + 10x) * (10 + 10x) 100 + 192x + 100x2 = (10(10 + 10x) + 10x * (10 + 10x)) + 8 100 + 192x + 100x2 = ((10 * 10 + 10x * 10) + 10x * (10 + 10x)) + 8 100 + 192x + 100x2 = ((100 + 100x) + 10x * (10 + 10x)) + 8 100 + 192x + 100x2 = (100 + 100x + (10 * 10x + 10x * 10x)) + 8 100 + 192x + 100x2 = (100 + 100x + (100x + 100x2)) + 8 Combine like terms: 100x + 100x = 200x 100 + 192x + 100x2 = (100 + 200x + 100x2) + 8 Reorder the terms: 100 + 192x + 100x2 = 100 + 8 + 200x + 100x2 Combine like terms: 100 + 8 = 108 100 + 192x + 100x2 = 108 + 200x + 100x2 Add '-100x2' to each side of the equation. 100 + 192x + 100x2 + -100x2 = 108 + 200x + 100x2 + -100x2 Combine like terms: 100x2 + -100x2 = 0 100 + 192x + 0 = 108 + 200x + 100x2 + -100x2 100 + 192x = 108 + 200x + 100x2 + -100x2 Combine like terms: 100x2 + -100x2 = 0 100 + 192x = 108 + 200x + 0 100 + 192x = 108 + 200x Solving 100 + 192x = 108 + 200x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-200x' to each side of the equation. 100 + 192x + -200x = 108 + 200x + -200x Combine like terms: 192x + -200x = -8x 100 + -8x = 108 + 200x + -200x Combine like terms: 200x + -200x = 0 100 + -8x = 108 + 0 100 + -8x = 108 Add '-100' to each side of the equation. 100 + -100 + -8x = 108 + -100 Combine like terms: 100 + -100 = 0 0 + -8x = 108 + -100 -8x = 108 + -100 Combine like terms: 108 + -100 = 8 -8x = 8 Divide each side by '-8'. x = -1 Simplifying x = -1
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