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Simplifying 6x(6x + 6) + -5 = 1 + 6x Reorder the terms: 6x(6 + 6x) + -5 = 1 + 6x (6 * 6x + 6x * 6x) + -5 = 1 + 6x (36x + 36x2) + -5 = 1 + 6x Reorder the terms: -5 + 36x + 36x2 = 1 + 6x Solving -5 + 36x + 36x2 = 1 + 6x Solving for variable 'x'. Reorder the terms: -5 + -1 + 36x + -6x + 36x2 = 1 + 6x + -1 + -6x Combine like terms: -5 + -1 = -6 -6 + 36x + -6x + 36x2 = 1 + 6x + -1 + -6x Combine like terms: 36x + -6x = 30x -6 + 30x + 36x2 = 1 + 6x + -1 + -6x Reorder the terms: -6 + 30x + 36x2 = 1 + -1 + 6x + -6x Combine like terms: 1 + -1 = 0 -6 + 30x + 36x2 = 0 + 6x + -6x -6 + 30x + 36x2 = 6x + -6x Combine like terms: 6x + -6x = 0 -6 + 30x + 36x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-1 + 5x + 6x2) = 0 Factor a trinomial. 6((-1 + -1x)(1 + -6x)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-1 + -1x)' equal to zero and attempt to solve: Simplifying -1 + -1x = 0 Solving -1 + -1x = 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 + -1x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1x = 0 + 1 -1x = 0 + 1 Combine like terms: 0 + 1 = 1 -1x = 1 Divide each side by '-1'. x = -1 Simplifying x = -1Subproblem 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 = {-1, 0.1666666667}
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