(x+3)^(x-0,5)<0 desigualdades

Se da la desigualdad:
$$\left(x + 3\right)^{x - \frac{1}{2}} < 0$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$\left(x + 3\right)^{x - \frac{1}{2}} = 0$$
Resolvemos:
$$x_{1} = -56.8872874671946 + 1.86032286071536 i$$
$$x_{2} = -44.9521384954488 + 1.99411544075916 i$$
$$x_{3} = -58.8778316729686 + 1.84178853387051 i$$
$$x_{4} = -25.1112449913453 + 2.38296540126348 i$$
$$x_{5} = -70.8271795602881 + 1.74632109061647 i$$
$$x_{6} = -17.2099600294603 + 2.68360824963445 i$$
$$x_{7} = -90.7597947338789 + 1.62836521591924 i$$
$$x_{8} = -38.4568396359062$$
$$x_{9} = -37.0056740772593 + 2.11433984600809 i$$
$$x_{10} = -86.7719420437028 + 1.64892420435825 i$$
$$x_{11} = -80.7913092192972 + 1.68232673946798 i$$
$$x_{12} = -29.0716551697201 + 2.27677304230924 i$$
$$x_{13} = -84.7782378772484 + 1.65969734320076 i$$
$$x_{14} = -100.731737978093 + 1.58198548327833 i$$
$$x_{15} = -94.748197958271 + 1.60901098994346 i$$
$$x_{16} = -60.8686957915994 + 1.82410112335934 i$$
$$x_{17} = -96.7425917333723 + 1.59974823628508 i$$
$$x_{18} = -92.7539304764517 + 1.61854526606096 i$$
$$x_{19} = -102.726481081352 + 1.57346172649423 i$$
$$x_{20} = -27.0907890733987 + 2.3272108918749 i$$
$$x_{21} = -82.7846910846935 + 1.67082461336369 i$$
$$x_{22} = -54.8970849606657 + 1.87977672254041 i$$
$$x_{23} = -42.9645965196765 + 2.02125093078451 i$$
$$x_{24} = -52.9072482013241 + 1.90023186656731 i$$
$$x_{25} = -62.8598600250948 + 1.80719586629625 i$$
$$x_{26} = -68.8349805874056 + 1.7606220710008 i$$
$$x_{27} = -35.0208051943819 + 2.15011351456698 i$$
$$x_{28} = -50.9178038200274 + 1.92178070237845 i$$
$$x_{29} = -9.30209197655335 + 3.17637619455067 i$$
$$x_{30} = -78.7981003801705 + 1.69422621080467 i$$
$$x_{31} = -15.239560885993 + 2.78730934459328 i$$
$$x_{32} = -76.8050732657004 + 1.70654748063028 i$$
$$x_{33} = -21.1568348174579 + 2.51469555556647 i$$
$$x_{34} = -23.1331952416106 + 2.44503812115936 i$$
$$x_{35} = -74.8122372336441 + 1.71931719375897 i$$
$$x_{36} = -40.9776350091113 + 2.05018417093157 i$$
$$x_{37} = -46.9402139813358 + 1.96859397083766 i$$
$$x_{38} = -31.0536948145328 + 2.23085313931056 i$$
$$x_{39} = -72.8196023689177 + 1.73256444732902 i$$
$$x_{40} = -64.8513063305415 + 1.79101479296641 i$$
$$x_{41} = -33.0367810289505 + 2.1888078226796 i$$
$$x_{42} = -13.2702976066491 + 2.90703330230029 i$$
$$x_{43} = -11.2979945746145 + 3.04260985646899 i$$
$$x_{44} = -38.9913072606523 + 2.08112971050121 i$$
$$x_{45} = -88.7657965290299 + 1.63848606181836 i$$
$$x_{46} = -66.8430182198927 + 1.77550583471965 i$$
$$x_{47} = -19.1823683930737 + 2.59354513602772 i$$
$$x_{48} = -48.9287814105527 + 1.94452816197746 i$$
$$x_{49} = -98.7371066805192 + 1.59074382927615 i$$
Descartamos las soluciones complejas:
$$x_{1} = -38.4568396359062$$
Las raíces dadas
$$x_{1} = -38.4568396359062$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} < x_{1}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$-38.4568396359062 + - \frac{1}{10}$$
=
$$-38.5568396359062$$
lo sustituimos en la expresión
$$\left(x + 3\right)^{x - \frac{1}{2}} < 0$$
$$\left(-38.5568396359062 + 3\right)^{-38.5568396359062 - \frac{1}{2}} < 0$$

-2.62350573786034e-61 + 4.73515095110676e-62*I < 0

Entonces
$$x < -38.4568396359062$$
no se cumple
significa que la solución de la desigualdad será con:
$$x > -38.4568396359062$$

         _____  
        /
-------ο-------
       x1