SOLUTION: Any help with these three would be appreciated. I keep thinking I've done them correctly but was actually wrong and I've gone around with them so much I think I've completely forg

Question 184824: Any help with these three would be appreciated. I keep thinking I've done them correctly but was actually wrong and I've gone around with them so much I think I've completely forgotten what I'm doing!
1. 3x2 + 11x � 20 = 0 Solve by factoring
2. x2 + 3x - 4 = 0 Solve by completing the squares
3. 3x2 � x � 1 = 0 Solve by graphing (preferably using Excel)

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
I'll do the first one to get you started. If you're still stuck, then feel free to repost

# 1

First, let's factor the left side :

Looking at the expression , we can see that the first coefficient is , the second coefficient is , and the last term is .

Now multiply the first coefficient by the last term to get .

Now the question is: what two whole numbers multiply to (the previous product) and add to the second coefficient ?

To find these two numbers, we need to list all of the factors of (the previous product).

Factors of :
1,2,3,4,5,6,10,12,15,20,30,60
-1,-2,-3,-4,-5,-6,-10,-12,-15,-20,-30,-60

Note: list the negative of each factor. This will allow us to find all possible combinations.

These factors pair up and multiply to .
1*(-60)
2*(-30)
3*(-20)
4*(-15)
5*(-12)
6*(-10)
(-1)*(60)
(-2)*(30)
(-3)*(20)
(-4)*(15)
(-5)*(12)
(-6)*(10)

Now let's add up each pair of factors to see if one pair adds to the middle coefficient :

First Number	Second Number	Sum
1	-60	1+(-60)=-59
2	-30	2+(-30)=-28
3	-20	3+(-20)=-17
4	-15	4+(-15)=-11
5	-12	5+(-12)=-7
6	-10	6+(-10)=-4
-1	60	-1+60=59
-2	30	-2+30=28
-3	20	-3+20=17
-4	15	-4+15=11
-5	12	-5+12=7
-6	10	-6+10=4

From the table, we can see that the two numbers and add to (the middle coefficient).

So the two numbers and both multiply to and add to

Now replace the middle term with . Remember, and add to . So this shows us that .

Replace the second term with .

Group the terms into two pairs.

Factor out the GCF from the first group.

Factor out from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis.

Combine like terms. Or factor out the common term

So factors to .

-----------------------------------------------

This means that transforms into

Start with the given equation.

Now set each factor equal to zero:

or

Let's solve the first equation

Subtract 5 from both sides to isolate "x".

So the first solution is

--------

Now let's solve the second equation

Add 4 to both sides.

Divide both sides by 3 to isolate "x".

So the second solution is

=========================================================

Answer:

So the solutions are

or
RELATED QUESTIONS
This is a different kind of question any advice would be appreciated. I�m planning to go... (answered by stanbon,ikleyn)

I've already answered these, but I need to ensure they are correct. Can someone please (answered by MathLover1)

Calculate: (-2/3*2%)^4*(-3/4*3%)^3*(-4/5*4%)^2*(-5/6*5%)*10^20 I’ve been trying to... (answered by ikleyn,MathLover1,MathTherapy)

Hello team, would you be so kind to assist with this problem below. I�ve tried to figure... (answered by Edwin McCravy)

I have been struggling with a word problem. The problem is "Best rentals charges a daily (answered by math_tutor2020,ikleyn,josgarithmetic,MathTherapy)

I am having trouble with these long equations, I know how to do them but I keep getting... (answered by stanbon)

A bacteria culture started with 6500 bacteria and increased by 35% in the first 2 hours.... (answered by ewatrrr)

Use polynomial division to determine: 3x^3-5x^2+10x+4 / 3x+1 Any help would be... (answered by stanbon,pmatei)

Hello everyone! I realize it is stated only one problem per submission, however, there... (answered by stanbon,edjones,richwmiller,wilft1)