Question

completando trinomio cuadrado perfecto de 25x2-5x-6=0

Answer 1

$25x^2-5x-6=0$

$\mathrm{Para\:}\quad a=25,\:b=-5,\:c=-6$

$\frac{-\left(-5\right)+\sqrt{\left(-5\right)^2-4\cdot \:25\left(-6\right)}}{2\cdot \:25}=\frac{5+\sqrt{\left(-5\right)^2-4\cdot \:25\left(-6\right)}}{2\cdot \:25}$
$=\frac{5+\sqrt{\left(-5\right)^2-\left(-6\right)\cdot \:4\cdot \:25}}{50}=\frac{5+\sqrt{25-\left(-6\right)\cdot \:100}}{50}$
$=\frac{5+25}{50}=\frac{30}{50}=\frac{3}{5}$


$\frac{-\left(-5\right)-\sqrt{\left(-5\right)^2-4\cdot \:25\left(-6\right)}}{2\cdot \:25}=\frac{5-\sqrt{\left(-5\right)^2-4\cdot \:25\left(-6\right)}}{2\cdot \:25}$
$=\frac{5-\sqrt{\left(-5\right)^2-\left(-6\right)\cdot \:4\cdot \:25}}{50}=\frac{5-\sqrt{25-\left(-6\right)\cdot \:100}}{50}$
$=\frac{5-25}{50}=-\frac{20}{50}=-\frac{2}{5}$


$x=\frac{3}{5},\:x=-\frac{2}{5}$