SOLUTION: im a little confused as to what to do with the exponent in this situation. My teacher taught us in class but now that im home my mind went blank. The answer i came up with is -1. B

Algebra ->  Equations -> SOLUTION: im a little confused as to what to do with the exponent in this situation. My teacher taught us in class but now that im home my mind went blank. The answer i came up with is -1. B      Log On


   

Question 285345: im a little confused as to what to do with the exponent in this situation. My teacher taught us in class but now that im home my mind went blank. The answer i came up with is -1. But the answers that were provided on this site are -2 and -4. Here is the problem: x^2 + 6x + 8 = 0 Here's what i did: x*x+6x+8=0 2x+6x+8=0 8x+8=0 8x=-8 x=-1...Someone just sent me an answer that just said factor (x+4)(x+2)=0....I'm even more confused now...IS THERE ANYONE THAT CAN BREAK THIS PROBLEM DOWN FOR ME STEP BY STEP PLEASE...THANK YOU!!
Found 2 solutions by jim_thompson5910, Deina:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
You made an error in thinking that x%2Ax=2x. This is NOT true, and is a big misconception. So x%2Ax%3C%3E2x for all 'x'. What you were thinking of (I think) is that x%2Bx=2x which is true for all 'x'.


There are two ways to solve this problem.

# 1 Factoring

First factor x%5E2+%2B+6x+%2B+8




Looking at the expression x%5E2%2B6x%2B8, we can see that the first coefficient is 1, the second coefficient is 6, and the last term is 8.


Now multiply the first coefficient 1 by the last term 8 to get %281%29%288%29=8.


Now the question is: what two whole numbers multiply to 8 (the previous product) and add to the second coefficient 6?


To find these two numbers, we need to list all of the factors of 8 (the previous product).


Factors of 8:
1,2,4,8
-1,-2,-4,-8


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


These factors pair up and multiply to 8.
1*8 = 8
2*4 = 8
(-1)*(-8) = 8
(-2)*(-4) = 8

Now let's add up each pair of factors to see if one pair adds to the middle coefficient 6:


First NumberSecond NumberSum
181+8=9
242+4=6
-1-8-1+(-8)=-9
-2-4-2+(-4)=-6



From the table, we can see that the two numbers 2 and 4 add to 6 (the middle coefficient).


So the two numbers 2 and 4 both multiply to 8 and add to 6


Now replace the middle term 6x with 2x%2B4x. Remember, 2 and 4 add to 6. So this shows us that 2x%2B4x=6x.


x%5E2%2Bhighlight%282x%2B4x%29%2B8 Replace the second term 6x with 2x%2B4x.


%28x%5E2%2B2x%29%2B%284x%2B8%29 Group the terms into two pairs.


x%28x%2B2%29%2B%284x%2B8%29 Factor out the GCF x from the first group.


x%28x%2B2%29%2B4%28x%2B2%29 Factor out 4 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.


%28x%2B4%29%28x%2B2%29 Combine like terms. Or factor out the common term x%2B2




So x%5E2%2B6x%2B8 factors to %28x%2B4%29%28x%2B2%29.


Since x%5E2%2B6x%2B8=%28x%2B4%29%28x%2B2%29 and x%5E2%2B6x%2B8=0, this means that %28x%2B4%29%28x%2B2%29=0




So we've gone from x%5E2%2B6x%2B8=0 to %28x%2B4%29%28x%2B2%29=0



Now remember that if AB = 0 (A times B equals zero), then either A=0, B=0 or both are equal to zero. This is the zero product property.


So use the zero product property to break %28x%2B4%29%28x%2B2%29=0 down into the following equations shown below:

x%2B4=0 or x%2B2=0


Now solve each equation to get

x=-4 or x=-2


So the two solutions are x=-4 or x=-2


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

Method # 2: Quadratic Formula




x%5E2%2B6x%2B8=0 Start with the given equation.


Notice that the quadratic x%5E2%2B6x%2B8 is in the form of Ax%5E2%2BBx%2BC where A=1, B=6, and C=8


Let's use the quadratic formula to solve for "x":


x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


x+=+%28-%286%29+%2B-+sqrt%28+%286%29%5E2-4%281%29%288%29+%29%29%2F%282%281%29%29 Plug in A=1, B=6, and C=8


x+=+%28-6+%2B-+sqrt%28+36-4%281%29%288%29+%29%29%2F%282%281%29%29 Square 6 to get 36.


x+=+%28-6+%2B-+sqrt%28+36-32+%29%29%2F%282%281%29%29 Multiply 4%281%29%288%29 to get 32


x+=+%28-6+%2B-+sqrt%28+4+%29%29%2F%282%281%29%29 Subtract 32 from 36 to get 4


x+=+%28-6+%2B-+sqrt%28+4+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%28-6+%2B-+2%29%2F%282%29 Take the square root of 4 to get 2.


x+=+%28-6+%2B+2%29%2F%282%29 or x+=+%28-6+-+2%29%2F%282%29 Break up the expression.


x+=+%28-4%29%2F%282%29 or x+=++%28-8%29%2F%282%29 Combine like terms.


x+=+-2 or x+=+-4 Simplify.


So the solutions are x+=+-2 or x+=+-4


Note: the order of the solutions does not matter.

Answer by Deina(147) About Me  (Show Source):
You can put this solution on YOUR website!
+x%5E2+%2B+6x+%2B+8+=+0+ is a quadratic equation, so use the
formula ax%5E2%2Bbx%2Bc=0

in this case we have:
a = 1
b = 6
c = 8
+x%5B1%2C2%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2a+
Notice that you will have two answers!
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B6x%2B8+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%286%29%5E2-4%2A1%2A8=4.

Discriminant d=4 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-6%2B-sqrt%28+4+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%286%29%2Bsqrt%28+4+%29%29%2F2%5C1+=+-2
x%5B2%5D+=+%28-%286%29-sqrt%28+4+%29%29%2F2%5C1+=+-4

Quadratic expression 1x%5E2%2B6x%2B8 can be factored:
1x%5E2%2B6x%2B8+=+1%28x--2%29%2A%28x--4%29
Again, the answer is: -2, -4. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B6%2Ax%2B8+%29


Quadratics have always been one of my favorite equations, because they are so much easier than factoring!
Go through the quadratic explanation above several times. Once you think you understand it, use some different numbers and see if you can calculate it out to the same answer the computer gives you until you're sure that you understand it. It will save you massive amounts of work in the future!
Once you understand the quadratic, bob's your uncle!