Answer: [tex]x=\frac{3}{5}+i\frac{4}{5},\:x=\frac{3}{5}-i\frac{4}{5}[/tex]
Step-by-step explanation:
[tex]25x^2-30x+25=0[/tex]
[tex]x_{1,\:2}=\frac{-\left(-30\right)\pm \sqrt{\left(-30\right)^2-4\cdot \:25\cdot \:25}}{2\cdot \:25}[/tex]
[tex]\sqrt{\left(-30\right)^2-4\cdot \:25\cdot \:25}[/tex]
[tex]=\sqrt{30^2-4\cdot \:25\cdot \:25}[/tex]
[tex]=\sqrt{30^2-2500}[/tex]
[tex]=i\sqrt{2500-30^2}[/tex]
[tex]=40i[/tex]
[tex]x_{1,\:2}=\frac{-\left(-30\right)\pm \:40i}{2\cdot \:25}[/tex]
[tex]x_1=\frac{-\left(-30\right)+40i}{2\cdot \:25},\:x_2=\frac{-\left(-30\right)-40i}{2\cdot \:25}[/tex]
[tex]x=\frac{3}{5}+i\frac{4}{5},\:x=\frac{3}{5}-i\frac{4}{5}[/tex]
