I was wondering if my answer is right.
Let f (x)=(x+10)^2. Find x so that f(x)=72
(x+10)^2=72
x^2+20x+100=72
x^2+20x+28=0
x=(-20+-sqrt(400-112))/2
x=-10+6*sqrt(2)
Yeap! Your answer looks good. Don't forget that the sign before your radical can be +/-, thus yielding two answers!
-10+6*sqrt(2) AND -10-6*sqrt(2)
Thank you for your help and reminding me there is two answers.
To verify if your answer is correct, we can substitute the value of x back into the original equation and check if it results in f(x) = 72.
Let's substitute x = -10 + 6√2 into the equation f(x) = (x+10)^2:
f(-10 + 6√2) = ((-10 + 6√2) + 10)^2
= (6√2)^2
= 36 * 2
= 72
As we can see, f(-10 + 6√2) does indeed equal 72. Therefore, your answer is correct.
To arrive at this answer, you correctly set up the equation (x+10)^2 = 72 and solved it correctly using the quadratic formula. Well done!