SOLUTION: Its been a while since I graduated high school, and I'm trying to refresh my memory on some math. I don't quite understand how to solve this problem, could you please help and expl

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Question 760474: Its been a while since I graduated high school, and I'm trying to refresh my memory on some math. I don't quite understand how to solve this problem, could you please help and explain it to me step by step?
Solve for t, f(t+1)=0, f(x)=x^2-7x+10
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
as far as i can tell, they wsnt you to replace x with t+1 and then solve for the roots of that equation.
you can do this in 2 ways.
you can solve for the roots of x^2 - 7x + 10 and then replace x with t+1, or you can replace x with t+1 and solve for the roots of that equation.
first method (solve for roots of x^2 - 7x + 10):
set the equation into the standard quadratic form of ax^2 + b2 + c = 0 to get:
x^2 - 7x + 10 = 0
factor this equation to get:
(x-5)*(x-2) = 0
solve for x to get:
x = 5
x = 2
replace x with t+1 to get:
t + 1 = 5
t + 1 = 2
solve for t to get:
t = 4
t = 1
second method (replace x with t+1 and then solve for the roots of that equation:
original equation is x^2 - 7x + 10
replace x with t+1 to get:
(t+1)^2 - 7(t+1) + 10
set this equation into standard quadratic form of at^2 + bt + c = 0 to get:
(t+1)^2 - 7(t+1) + 10 = 0
simplify this equation to get:
t^2 + 2t + 1 - 7t - 7 + 10 = 0
simplify further to get:
t^2 - 5t + 4 = 0
factor this equation to get:
(t-4) * (t-1) = 0
solve for t to get:
t = 4
t = 1
a graph of both equations is shown below:

in order to graph the t equation, i had to change the variable name to x.
that didn't impact the equation at all but allowed it to be graphed using the graphing software from algebra.com.
both methods will arrive at the same value for t.
you need to know how to factor quadratic equations and you need to know the standard form of quadratic equations and you should know the quadratic formula at least. you should also probably know factoring by least square method as well.
get a high school algebra book or look online for references to quadratic equations and how to solve them.
a search on google usually puts up a whole slew of them.
pick the ones that look like they're the easiest for you to understand.
some websites that i've used for review that are pretty good are:
http://www.wtamu.edu/academic/anns/mps/math/mathlab/
http://www.purplemath.com/
http://www.regentsprep.org/
there are others, including www.algebra.com where you can look at the lessons made by tutors and you can scan for previous problems of the type you are interested in that were previously solved.