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Simplifying 6(7x + 6)(7x + 6) + 42(6x + 7)(7x + 6) = 0 Reorder the terms: 6(6 + 7x)(7x + 6) + 42(6x + 7)(7x + 6) = 0 Reorder the terms: 6(6 + 7x)(6 + 7x) + 42(6x + 7)(7x + 6) = 0 Multiply (6 + 7x) * (6 + 7x) 6(6(6 + 7x) + 7x * (6 + 7x)) + 42(6x + 7)(7x + 6) = 0 6((6 * 6 + 7x * 6) + 7x * (6 + 7x)) + 42(6x + 7)(7x + 6) = 0 6((36 + 42x) + 7x * (6 + 7x)) + 42(6x + 7)(7x + 6) = 0 6(36 + 42x + (6 * 7x + 7x * 7x)) + 42(6x + 7)(7x + 6) = 0 6(36 + 42x + (42x + 49x2)) + 42(6x + 7)(7x + 6) = 0 Combine like terms: 42x + 42x = 84x 6(36 + 84x + 49x2) + 42(6x + 7)(7x + 6) = 0 (36 * 6 + 84x * 6 + 49x2 * 6) + 42(6x + 7)(7x + 6) = 0 (216 + 504x + 294x2) + 42(6x + 7)(7x + 6) = 0 Reorder the terms: 216 + 504x + 294x2 + 42(7 + 6x)(7x + 6) = 0 Reorder the terms: 216 + 504x + 294x2 + 42(7 + 6x)(6 + 7x) = 0 Multiply (7 + 6x) * (6 + 7x) 216 + 504x + 294x2 + 42(7(6 + 7x) + 6x * (6 + 7x)) = 0 216 + 504x + 294x2 + 42((6 * 7 + 7x * 7) + 6x * (6 + 7x)) = 0 216 + 504x + 294x2 + 42((42 + 49x) + 6x * (6 + 7x)) = 0 216 + 504x + 294x2 + 42(42 + 49x + (6 * 6x + 7x * 6x)) = 0 216 + 504x + 294x2 + 42(42 + 49x + (36x + 42x2)) = 0 Combine like terms: 49x + 36x = 85x 216 + 504x + 294x2 + 42(42 + 85x + 42x2) = 0 216 + 504x + 294x2 + (42 * 42 + 85x * 42 + 42x2 * 42) = 0 216 + 504x + 294x2 + (1764 + 3570x + 1764x2) = 0 Reorder the terms: 216 + 1764 + 504x + 3570x + 294x2 + 1764x2 = 0 Combine like terms: 216 + 1764 = 1980 1980 + 504x + 3570x + 294x2 + 1764x2 = 0 Combine like terms: 504x + 3570x = 4074x 1980 + 4074x + 294x2 + 1764x2 = 0 Combine like terms: 294x2 + 1764x2 = 2058x2 1980 + 4074x + 2058x2 = 0 Solving 1980 + 4074x + 2058x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(330 + 679x + 343x2) = 0 Factor a trinomial. 6((55 + 49x)(6 + 7x)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(55 + 49x)' equal to zero and attempt to solve: Simplifying 55 + 49x = 0 Solving 55 + 49x = 0 Move all terms containing x to the left, all other terms to the right. Add '-55' to each side of the equation. 55 + -55 + 49x = 0 + -55 Combine like terms: 55 + -55 = 0 0 + 49x = 0 + -55 49x = 0 + -55 Combine like terms: 0 + -55 = -55 49x = -55 Divide each side by '49'. x = -1.12244898 Simplifying x = -1.12244898Subproblem 2
Set the factor '(6 + 7x)' equal to zero and attempt to solve: Simplifying 6 + 7x = 0 Solving 6 + 7x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + 7x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 7x = 0 + -6 7x = 0 + -6 Combine like terms: 0 + -6 = -6 7x = -6 Divide each side by '7'. x = -0.8571428571 Simplifying x = -0.8571428571Solution
x = {-1.12244898, -0.8571428571}
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