Give the quadratic function f(x) = 25x^2-100x+100, find value of x such that f(x) = 25?

1.) f(x) = 25x²-100x+100

f(x) = 25

25x²-100x+100 = 25

25x²-100x+75 = 0

25(x-3)(x-1) = 0

x-3 = 0 or x-1 = 0

x = 3 or x = 1

Solutions: x = 1 or x = 3

2.) 625x²-2500x+2500 = 0

625(x-2)² = 0

x-2 = 0

x = 2

Solution: x = 2

I am assuming that the question is that in bold type and the rest is your answer which you would like checked.

Please note that f(25) is not the same as f(x)=25

f(25) means that x = 25 is substituted into the rule of f(x) but

f(x)=25 means that the rule 25x² - 100x + 100 = 25 ....this can be solved to find the x-value

=> 25x² - 100x + 100 = 25

=> 25x² - 100x + 75 = 0 ...................divide thru by common factor of 25 to get

=> x² - 4x + 3 = 0 ..........factorising (want factors of +3 that add to -4 , ie -3 and -1)

=> x² - x - 3x + 3 = 0 ......factorise 1st two terms then last two terms on LHS

=> x(x - 1) -3(x - 1) = 0 ..........take out as a factor the repeated factor of (x-1)

=> (x - 1)(x - 3) = 0

=> x - 1 = 0 or x - 3 = 0

=> x = 1 or x = 3

as f(x) =25

set 25x^2-100x+100 =25

=

25x^2-100x+75=0

now you can use the quadratic equation to find out the values of x which are true for this equation