Question 66056This question is from textbook beginning algebra
: I'm supposed to solve for the roots of each quadratic equation by using the factoring method. This is so confusing to me it's almost painful. I honestly d^2+3x-40=0 on't know where to start.
Xis the problem. If you could get this to make sense to me I would greatly appreciate it.
Karen
This question is from textbook beginning algebra
Found 3 solutions by algebrapro18, ptaylor, josmiceli:
Answer by algebrapro18(249)   (Show Source):
You can put this solution on YOUR website! Well to solve a quadratic equation by factoring you need to do the following:
1)Factor the quadratic equation
a)Multiply the a and c terms together where a and c are coefficients.
b)Factor that number and see what factors add to the b term.
*Note: You might end up haveing to take the negative of both factors to get
them to add right.
c)re-write the equation as a product of its factors.
2)Set each factor equal to 0 and solve
X^2+3x-40=0
a = 1, b= 3, c = -40
a * c = 1 * -40 = -40
factors of -40 are:
-1 and 40
-2 and 20
-4 and 10
-5 and 8
-5 * 8 = -40
-5 + 8 = 3
X^2+3x-40=0
=>(x-5)(x+8)=0
now solve each equation
x - 5 = 0
x = 5
x + 8 = 0
x = -8
So the solution to X^2+3x-40=0 are x = 5 and x = -8 now we check our work
5^2+3(5)-40=0
25+15-40=0
0=0 so we know that x = 5 is a solution.
(-8)^2+3(-8)-40=0
64-24-40=0
0=0 so we know that x = -8 is a solution and we are done.
Answer by ptaylor(2198)  (Show Source):
You can put this solution on YOUR website! I'm supposed to solve for the roots of each quadratic equation by using the factoring method. This is so confusing to me it's almost painful. I honestly don't know where to start.
X^2+3x-40=0 is the problem. If you could get this to make sense to me I would greatly appreciate it.
Factor:
x^2+3x-40=0
This quadratic is in the form ax^2+bx+c=0
where: a=1
b=3
c=-40
When a=1, then, if it is factorable, the sum of the products of c must equal b
what are the products of -40 that equals +3, are they:
-10 time +4 ------------no
-2 times +20--------------no
-40 times +1---------------no
-8 times +5-----------no
+8 times -5-------------BINGO!!!!!!!!!!!!!!!
Soooo(x+8)(x-5)=0 (Multiplying it out: x^2-5x+8x-40=x^2+3x-40)
x+8=0
x=-8 and
x-5=0
x=+5
Hope this helps--------------ptaylor
Answer by josmiceli(19441)  (Show Source):
You can put this solution on YOUR website! You have either one of two problems
Either you have:
(1) The blank stare mental paralysis drifting off to daydream problem
or, almost as bad
(2) The jump in with both feet without a plan problem
(2) usually leads to (1)
Start off with what you know for sure. You know the answer will
generally look like this:
(_____plus or minus_____)(_____plus or minus_____) = 0
I recommend you do just what I did. Write down the
parentheses with nothing in them yet and the "= 0"
Now figure out what the signs should be. Look at
the problem.  . There's only two ways you can get
the  , + times -, or, - times +, so put in one of those.
(____ + ____)(____ - ____) = 0. This is what you know for sure so far.
and you can do it with any factoring problem. Lots better than a blank
stare.
Now look at the  . The factors are  and . If it was
say,  , the factors might be  and  or
 and , but your problem is easier.
OK, so far you have
( x + ____)( x - ____) = 0
Now you have to do a little head-scratching, but it's really not that bad.
All you need to remember about factoring is that each term in the first
gets multiplied by each term in the second, so if I had
(a + b)(c + d - e + f) I'd get ac + ad - ae + af + bc + bd - be + bf
Look at the middle term,  , The sign is positive. That means
that whatever factors you decide on for the , the + factor should
be the greatest. Look at all the possibilities
But I said the greatest factor should be +, so that leaves us
Try these one by one and see what the middle term ends up being
( x + 40)( x - 1) = 0
so, that's not it
(x + 20)(x - 2) = 0
Closer, but that's not it either
(x + 10)(x - 4) = 0
Closest so far, still not right
(x + 8)(x - 5) = 0
Bingo! Just go step by step. Notice that 8 - 5 = 3 is the key, but
going step by step will always get you there with no blank stares.
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