Question #5cc93

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Answer 1 · 2017-04-15T01:54:37

$x = \frac{1}{3}$ $x=1/3$

$x = - \frac{2}{3} \pm i$ $x=-2/3+-i$

Subtract $13$ $13$ from both sides

$27 x^{3} + 27 x^{2} + 27 x - 13 = 0$ $27x^3+27x^2+27x-13=0$

This can factored

$(3 x - 1) (9 x^{2} + 12 x + 13) = 0$ $(3x-1)(9x^2+12x+13)=0$

So,

$3 x - 1 = 0$ $3x-1=0$

$3 x = 1$ $3x=1$

$x = \frac{1}{3}$ $x=1/3$

$9 x^{2} + 12 x + 13 = 0$ $9x^2+12x+13=0$

$\frac{- 12 \pm \sqrt{{(12)}^{2} - 4 (9) (13)}}{2 (9)}$ $(-12+-sqrt((12)^2-4(9)(13)))/(2(9))$

$\frac{- 12 \pm \sqrt{144 - 468}}{18}$ $(-12+-sqrt(144-468))/18$

$\frac{- 12 \pm \sqrt{324} i}{18}$ $(-12+-sqrt(324)i)/18$

$- \frac{12}{18} \pm \frac{18 i}{18}$ $-12/18+-(18i)/18$

$- \frac{2}{3} \pm i$ $-2/3+-i$