SOLUTION: I'm trying to refresh myself, but don't know how to start. 1. 1/3 +2 2. (t-3)(t + 5)=9 3. (x-3)^2 + (x+2)^2=17 4. a^3 +3a^2 -25a = 75

Algebra ->  Algebra  -> Expressions -> SOLUTION: I'm trying to refresh myself, but don't know how to start. 1. 1/3 +2 2. (t-3)(t + 5)=9 3. (x-3)^2 + (x+2)^2=17 4. a^3 +3a^2 -25a = 75      Log On

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Question 44076: I'm trying to refresh myself, but don't know how to start.
1. 1/3 +2
2. (t-3)(t + 5)=9
3. (x-3)^2 + (x+2)^2=17
4. a^3 +3a^2 -25a = 75
Answer by adamchapman(301) About Me  (Show Source):
You can put this solution on YOUR website!
1.
make sure the denominators are identical
1%2F3%2B2=1%2F3%2B6%2F3=7%2F3
2.
Firstly, expand your brackets.
Remember the word FOIL. It stands for: Firsts, Outers, Inners, Lasts.
Take (a+b)(c+d)for example add the products of F.O.I.L:
%28a%2Bb%29%28c%2Bd%29=+ac+%2B+ad+%2B+bc+%2B+bd
In your question
a=t
b=-3
c=t
d=5
So:
%28t-3%29%28t+%2B+5%29=t%5E2%2B5t-3t-15=9
Now rearrange to give zero on the right hand side of a quadratic expression.
t%5E2%2B5t-3t-24=0
t%5E2%2B2t-24=0
Use the quadratic solver x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
where
a=1
b=2
c=-24
Now:
x+=+%28-2+%2B-+sqrt%28+2%5E2-4%2A1%2A%28-24%29+%29%29%2F%282%2A1%29+
x+=+%28-2+%2B-+sqrt%28+4%2B56+%29%29%2F2+
x+=+-1+%2B-+sqrt%28+60%29%2F2+
3.
%28x-3%29%5E2+%2B+%28x%2B2%29%5E2=17
Simplify:
%28x-3%29%28x-3%29+%2B+%28x%2B2%29%28x%2B2%29=17
using FOIL:
%28x%5E2-6x%2B9%29%2B%28x%5E2%2B4x%2B4%29=17
2x%5E2-2x%2B13=17
2x%5E2-2x-4=0
Now using the quadrastic solver again where
a=2
b=-2
c=-4
x=1+%2B-+sqrt%2836%29%2F2
4.
The method for solving cubic equations is very long. refer to http://www.sosmath.com/algebra/factor/fac11/fac11.html
for an explanation and examples
I hope this helps
P.S. I am trying to start up my own homework help website. I would be extremely grateful if you would e-mail me some feedback on the help you received to adam.chapman@student.manchester.ac.uk