for these three equations
x^2-4x+3=0
x^2-7x+2=20
x^2-3x=1
solve at least one by factoring
solve at least one by using the quadratic formula
solve the last one with either of the two options

- anonymous

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- anonymous

solve the second one by factoring and the last one by factoring also the first one you need to solve with quad eq.

- anonymous

First of all they all need to = 0.
The first two should be factoring.. the last one is quadratic formula.

- anonymous

x^2 - 4x + 3 = 0 Hint (3 * 1 = 3) (3 + 1 = 4)

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## More answers

- anonymous

1. (x - 3)(x - 1)

- anonymous

yea hes right i copied in diff order

- anonymous

x^2 - 7x + 2 = 20
x^2 - 7x - 18 = 0 Factors of 18 that subtract to give you 7
What are they?

- anonymous

x^2 - 3x - 1 = 0 the reason you use the quadratic formula is because there are no factors of 1 that subtract to give you 3.

- anonymous

Confused.. what are the solutions to #1 if (x - 3)(x - 1) = 0

- anonymous

3 and 1????

- anonymous

Very good

- anonymous

Now on the 2nd one... the factors of 18 are
1 * 18
2 * 9
3 * 6
which pair subtracts to give you 7

- anonymous

2 and 9

- anonymous

good so you have (x - 9)(x + 2) = 0
what would be your answers for x

- anonymous

9 and-2

- anonymous

Very good.
Now we need to do the quadratic formula.. do you know what that is? yes/no

- anonymous

i think so
ax^2+bx+c

- anonymous

well.. you have to get it in this form first.. so we have
x^2 - 3x - 1 = 0
what are
a?
b?
c?

- anonymous

a=1
b=-3
c=-1

- anonymous

Good.
the formula is
x = -b +- sqrt(b^2 - 4ac) all over 2a
Have you seen this the +- means a + with a - sign under it.

- anonymous

yes

- anonymous

-b I like to read as the opposite of b so the opposite of -3 is +3

- anonymous

x = 3 +- sqrt((-3)^2 - 4(1)(-1)
------------------------
2(1)

- anonymous

x = 3 +- sqrt(9 +4)
-------------
2
do you see how I got this? the (-4)(1)(-1) is a + 4

- anonymous

yes

- anonymous

OK.. so your answer is
x = 3 +- sqrt(13)
-----------
2

- anonymous

so 4.80 and 1.20

- anonymous

I don't think so..

- anonymous

If you are using a calculator put in
(3 + sqrt(13))/2
(3 - sqrt(13))/2

- anonymous

3.307

- anonymous

-3.027

- anonymous

Oops.. -.3027

- myininaya

but those aren't the answers those are approximations since the sqrt(13) is irrational

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