Question

How do you solve `x^2-10x+25=196`?

Answer 1

See explanation...

Explanation:

`x^2-10x+25=196`
In order to solve quadratic equation you have to make it equal to zero.
`x^2-10x+25-196=0`
`x^2-10x-171=0`

Then calculate the discriminant:
#[DELTA]=b^2-4*a*c =(-10)^2-4*1*(-171)= =100+684= =784#
*DELTA iz a sign for discriminant.

Write a quadratic formula and input all numbers in it, and solve for x1,2.

`x1,2= (-b +- sqrt(DELTA))/(2a)`
`x1,2=(-(-10) +- sqrt(784))/(2*1)`
`x1,2=(10 +- 28)/2`
`x1=(10+28)/2=38/2=19`
`x2=(10-28)/2=-18/2=-9`

Accordingly, there are two roots since the equation is quadratic.
The roots are: `x1=19` and `x2=-9`.