Question

Use the quadratic formula to solve the equation 25x^2-30x+25=0

Answer 1

Answer: $x=\frac{3}{5}+i\frac{4}{5},\:x=\frac{3}{5}-i\frac{4}{5}$

Step-by-step explanation:

$25x^2-30x+25=0$

$x_{1,\:2}=\frac{-\left(-30\right)\pm \sqrt{\left(-30\right)^2-4\cdot \:25\cdot \:25}}{2\cdot \:25}$

$\sqrt{\left(-30\right)^2-4\cdot \:25\cdot \:25}$

$=\sqrt{30^2-4\cdot \:25\cdot \:25}$

$=\sqrt{30^2-2500}$

$=i\sqrt{2500-30^2}$

$=40i$

$x_{1,\:2}=\frac{-\left(-30\right)\pm \:40i}{2\cdot \:25}$

$x_1=\frac{-\left(-30\right)+40i}{2\cdot \:25},\:x_2=\frac{-\left(-30\right)-40i}{2\cdot \:25}$

$x=\frac{3}{5}+i\frac{4}{5},\:x=\frac{3}{5}-i\frac{4}{5}$