You can
put this solution on YOUR website!First, we need to factor
Start with the given expression.
Factor out the GCF
.
Now let's try to factor the inner expression
---------------------------------------------------------------
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
:
1,2,7,14
-1,-2,-7,-14
Note: list the negative of each factor. This will allow us to find all possible combinations.
These factors pair up and multiply to
.
1*(-14) = -14
2*(-7) = -14
(-1)*(14) = -14
(-2)*(7) = -14
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 | -14 | 1+(-14)=-13 |
| 2 | -7 | 2+(-7)=-5 |
| -1 | 14 | -1+14=13 |
| -2 | 7 | -2+7=5 |
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
then factors further to
So
completely factors to
.
In other words,
.
-----------------------------------------------------------
Now let's use the factorization above to solve
Start with the given equation
Factor the left side (see above)
Now set each factor equal to zero:
or
or
Now solve for x in each case
==================================================================
Answer:
So the solutions are
or
You can
put this solution on YOUR website!I need help with sloving quadractic equations by factoring:
Step 1. Multiply by -1 to get rid of negative in x-squared term.
Step 2. We need two integers m an n such that their products is n*m=-2*7=-14 and their sum n+m= -13.
After several tries, these numbers are -14 and 1.
Step 3. Express -13x as -13x=-14x+1x=-14x+x and replace this in Step 1.
Step 4. Factor out 2x in the first group with parenthesis
Step 5. Factor out x-7 common to the groups with parenthesis
Step 6. The above equation yields two solutions as follows:
and
and
As a check, let's use the quadratic formula given below and solve
| Solved by pluggable solver: SOLVE quadratic equation with variable |
Quadratic equation  (in our case  ) has the following solutons:
For these solutions to exist, the discriminant  should not be a negative number.
First, we need to compute the discriminant :  .
Discriminant d=225 is greater than zero. That means that there are two solutions:  .
Quadratic expression  can be factored:
Again, the answer is: 7, -0.5.
Here's your graph:
 |
Same result as before.
Step 7. ANSWER. The solutions are
and
I hope the above steps were helpful.
For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.
Good luck in your studies!
Respectfully,
Dr J
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