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

1 Answer
Ratnaker Mehta
Jun 20, 2016

#:. 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!

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