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Simplifying (12x + -6)(12x + -6) = 16 Reorder the terms: (-6 + 12x)(12x + -6) = 16 Reorder the terms: (-6 + 12x)(-6 + 12x) = 16 Multiply (-6 + 12x) * (-6 + 12x) (-6(-6 + 12x) + 12x * (-6 + 12x)) = 16 ((-6 * -6 + 12x * -6) + 12x * (-6 + 12x)) = 16 ((36 + -72x) + 12x * (-6 + 12x)) = 16 (36 + -72x + (-6 * 12x + 12x * 12x)) = 16 (36 + -72x + (-72x + 144x2)) = 16 Combine like terms: -72x + -72x = -144x (36 + -144x + 144x2) = 16 Solving 36 + -144x + 144x2 = 16 Solving for variable 'x'. Reorder the terms: 36 + -16 + -144x + 144x2 = 16 + -16 Combine like terms: 36 + -16 = 20 20 + -144x + 144x2 = 16 + -16 Combine like terms: 16 + -16 = 0 20 + -144x + 144x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(5 + -36x + 36x2) = 0 Factor a trinomial. 4((1 + -6x)(5 + -6x)) = 0 Ignore the factor 4.Subproblem 1
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 = 0.1666666667Subproblem 2
Set the factor '(5 + -6x)' equal to zero and attempt to solve: Simplifying 5 + -6x = 0 Solving 5 + -6x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -6x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -6x = 0 + -5 -6x = 0 + -5 Combine like terms: 0 + -5 = -5 -6x = -5 Divide each side by '-6'. x = 0.8333333333 Simplifying x = 0.8333333333Solution
x = {0.1666666667, 0.8333333333}
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