Question

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

Answer 1

Answer:
`x=(3)/(5)+i(4)/(5),\:x=(3)/(5)-i(4)/(5)`

Explanation:

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

`x_(1,\:2)=(-\left(-30\right)\pm √(\left(-30\right)^2-4\cdot \:25\cdot \:25))/(2\cdot \:25)`

`√(\left(-30\right)^2-4\cdot \:25\cdot \:25)`

`=√(30^2-4\cdot \:25\cdot \:25)`

`=√(30^2-2500)`

`=i√(2500-30^2)`

`=40i`

`x_(1,\:2)=(-\left(-30\right)\pm \:40i)/(2\cdot \:25)`

`x_1=(-\left(-30\right)+40i)/(2\cdot \:25),\:x_2=(-\left(-30\right)-40i)/(2\cdot \:25)`

`x=(3)/(5)+i(4)/(5),\:x=(3)/(5)-i(4)/(5)`