Question #918e5

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Answer 1 · 2017-04-09T14:22:01

$x = - \frac{1}{2} \pm \sqrt{\frac{1}{4} - ln 2}$ $x =-1 /2+-sqrt (1/4 - ln 2)$
or
$x = - 0.500 \pm 0.666 i$ $x = -0.500+-0.666i$

$ln 2 - x - ln 4 - x^{2} = 0$ $ln 2 -x - ln 4 - x^2 =0$

$ln 2 - ln 4 = x^{2} + x$ $ln 2 - ln 4 = x^2 + x$

$ln 2 - {ln 2}^{2} = x^{2} + x$ $ln 2 - ln 2^2 = x^2 + x$

$ln 2 - 2 ln 2 = x^{2} + x$ $ln 2 - 2 ln 2 = x^2 + x$

$- ln 2 = x^{2} + x$ $- ln 2 = x^2 + x$

$- ln 2 = {(x + \frac{1}{2})}^{2} - {(\frac{1}{2})}^{2}$ $- ln 2 = (x + 1/2)^2 - (1/2)^2$

$\frac{1}{4} - ln 2 = {(x + \frac{1}{2})}^{2}$ $1/4 - ln 2 = (x + 1/2)^2$

$\pm \sqrt{\frac{1}{4} - ln 2} = x + \frac{1}{2}$ $+-sqrt (1/4 - ln 2) = x + 1/2$

$- \frac{1}{2} \pm \sqrt{\frac{1}{4} - ln 2} = x$ $-1 /2+-sqrt (1/4 - ln 2) = x$

$- 0.500 \pm \sqrt{0.250 - 0.693} = x$ $-0.500+-sqrt (0.250 - 0.693) = x$

$- 0.500 \pm \sqrt{- 0.443} = x$ $-0.500+-sqrt ( - 0.443) = x$

$- 0.500 \pm \sqrt{0.443 \cdot (- 1)} = x$ $-0.500+-sqrt ( 0.443 * (-1)) = x$

$- 0.500 \pm \sqrt{0.443 \cdot (i^{2})} = x$ $-0.500+-sqrt ( 0.443 * (i^2)) = x$ , where $i^{2} = - 1$ $i^2 = -1$

$- 0.500 \pm \sqrt{0.443} i = x$ $-0.500+-sqrt ( 0.443 )i = x$

$- 0.500 \pm 0.666 i = x$ $-0.500+-0.666i = x$