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Simplifying (6x + 2)(6x + 2) = 1 Reorder the terms: (2 + 6x)(6x + 2) = 1 Reorder the terms: (2 + 6x)(2 + 6x) = 1 Multiply (2 + 6x) * (2 + 6x) (2(2 + 6x) + 6x * (2 + 6x)) = 1 ((2 * 2 + 6x * 2) + 6x * (2 + 6x)) = 1 ((4 + 12x) + 6x * (2 + 6x)) = 1 (4 + 12x + (2 * 6x + 6x * 6x)) = 1 (4 + 12x + (12x + 36x2)) = 1 Combine like terms: 12x + 12x = 24x (4 + 24x + 36x2) = 1 Solving 4 + 24x + 36x2 = 1 Solving for variable 'x'. Reorder the terms: 4 + -1 + 24x + 36x2 = 1 + -1 Combine like terms: 4 + -1 = 3 3 + 24x + 36x2 = 1 + -1 Combine like terms: 1 + -1 = 0 3 + 24x + 36x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(1 + 8x + 12x2) = 0 Factor a trinomial. 3((1 + 2x)(1 + 6x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(1 + 2x)' equal to zero and attempt to solve: Simplifying 1 + 2x = 0 Solving 1 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2x = 0 + -1 2x = 0 + -1 Combine like terms: 0 + -1 = -1 2x = -1 Divide each side by '2'. x = -0.5 Simplifying x = -0.5Subproblem 2
Set the factor '(1 + 6x)' equal to zero and attempt to solve: Simplifying 1 + 6x = 0 Solving 1 + 6x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 6x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 6x = 0 + -1 6x = 0 + -1 Combine like terms: 0 + -1 = -1 6x = -1 Divide each side by '6'. x = -0.1666666667 Simplifying x = -0.1666666667Solution
x = {-0.5, -0.1666666667}
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