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Simplifying 12x2 = 1 + -4x Solving 12x2 = 1 + -4x Solving for variable 'x'. Reorder the terms: -1 + 4x + 12x2 = 1 + -4x + -1 + 4x Reorder the terms: -1 + 4x + 12x2 = 1 + -1 + -4x + 4x Combine like terms: 1 + -1 = 0 -1 + 4x + 12x2 = 0 + -4x + 4x -1 + 4x + 12x2 = -4x + 4x Combine like terms: -4x + 4x = 0 -1 + 4x + 12x2 = 0 Factor a trinomial. (-1 + -2x)(1 + -6x) = 0Subproblem 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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