Question

Calcula los dos valores de x para la ecuación: 4a^2 + 9a + 5 = 0

me ayudan porfavor​

Answer 1

Respuesta:

a1 = -1

a2 = -5/4

Explicación paso a paso:

$4a^2 + 9a + 5 = 0 \\\\ \mathrm{Resolver \: con \: la \: formula \: general \: para \: ecuaciones} \\ \mathrm{de \: segundo \: grado} \\\\ \boxed{x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}}$

$\mathrm{Para} \quad a = 4, \: b = 9, \: c = 5 \\\\ \boxed{a_{1,\:2}=\frac{-9\pm \sqrt{9^2-4\cdot 4\cdot 5}}{2\cdot 4}}$

$a_{1,\:2}=\frac{-9\pm \sqrt{9^2-4\cdot 4\cdot 5}}{2\cdot 4} \\\\ a_{1,\:2}=\frac{-9\pm \sqrt{9^2-80}}{2\cdot 4} \\\\ a_{1,\:2}=\frac{-9\pm \sqrt{81-80}}{2\cdot 4} \\\\ a_{1,\:2}=\frac{-9\pm \sqrt{81-80}}{2\cdot 4} \\\\ a_{1,\:2}=\frac{-9\pm \sqrt{1}}{2\cdot 4} \\\\ a_{1,\:2}=\frac{-9\pm 1}{2\cdot 4}$

$\mathrm{Separar \: las \: soluciones} \\\\ a_{1} = \frac{-9+1}{2 \cdot 4} \quad \& \quad a_{2} = \frac{-9-1}{2\cdot 4} \\\\\\ a_{1} = \frac{-9+1}{2 \cdot 4} \\\\ a_{1} = \frac{-8}{8} \\\\ \boxed{a_{1} = -1} \\\\\\ a_{2} = \frac{-9-1}{2 \cdot 4} \\\\ a_{2} = \frac{-10}{8} \\\\ a_{2} = \frac{-5}{4} \\\\ \boxed{a_{2} = -\frac{5}{4}}$