Question

Given the quadratic function f(x) = x^2 - 12x + 36 how do you find a value of x such that f(x) = 25?

Answer 1

`:. x=11, x=1.`

Explanation:

`f(x)=25`
`:. x^2-12x+36=25.`
`:. x^2-12x+36-25=0.`
`:. x^2-12x+11=0.`
`:. x^2-11x-1x+11=0.`.........`[11xx1=11,11+1=12]`
`:. x(x-11)-1(x-11)=0.`
`:. (x-11)(x-1)=0.`
`:. x=11, x=1.`

Alternatively, we see that `f(x)=(x-6)^2.`
Hence, `f(x)=25`
`rArr (x-6)^2=25=5^2.`
`rArr (x-6)=+-5`
`rArr x=6+-5`
`rArr x=11, or, x=1,` as before!