Question 909572: Question: A rectangle has an area of 330 meters squared. one side is 7 meters longer than the other. what are the dimensions of the rectangle?
My Attempt: x(x+7) = 330
x^2 + 7x = 330
square root both sides x + 7x = 18.2
8x/8 = 18.2/8
x = 2.25
It's wrong.
Found 2 solutions by JulietG, richwmiller:
Answer by JulietG(1812)   (Show Source):
You can put this solution on YOUR website! Area = length * width
A = 330m^2
330 = x(x+7)
330 = x^2 + 7x
Subtract 330 from each side
x^2 + 7x -330 = 0
Factor
(x+22)(x-15)
Since a measurement can't be a negative number, the only possibility is 15.
One side is 15. Therefore the other side is 22.
22 * 15 = 330
22 is 7 more than 15.
Answer by richwmiller(17219)  (Show Source):
You can put this solution on YOUR website! x + 7x = 18.2
How is x + 7x the same as  ?
x^2 + 7x = 330
x^2 + 7x - 330=0
Try to factor
Dismiss negative answers for measurements.
| Solved by pluggable solver: Factoring using the AC method (Factor by Grouping) |
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 :
1,2,3,5,6,10,11,15,22,30,33,55,66,110,165,330
-1,-2,-3,-5,-6,-10,-11,-15,-22,-30,-33,-55,-66,-110,-165,-330
Note: list the negative of each factor. This will allow us to find all possible combinations.
These factors pair up and multiply to .
1*(-330) = -330
2*(-165) = -330
3*(-110) = -330
5*(-66) = -330
6*(-55) = -330
10*(-33) = -330
11*(-30) = -330
15*(-22) = -330
(-1)*(330) = -330
(-2)*(165) = -330
(-3)*(110) = -330
(-5)*(66) = -330
(-6)*(55) = -330
(-10)*(33) = -330
(-11)*(30) = -330
(-15)*(22) = -330
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 | -330 | 1+(-330)=-329 | | 2 | -165 | 2+(-165)=-163 | | 3 | -110 | 3+(-110)=-107 | | 5 | -66 | 5+(-66)=-61 | | 6 | -55 | 6+(-55)=-49 | | 10 | -33 | 10+(-33)=-23 | | 11 | -30 | 11+(-30)=-19 | | 15 | -22 | 15+(-22)=-7 | | -1 | 330 | -1+330=329 | | -2 | 165 | -2+165=163 | | -3 | 110 | -3+110=107 | | -5 | 66 | -5+66=61 | | -6 | 55 | -6+55=49 | | -10 | 33 | -10+33=23 | | -11 | 30 | -11+30=19 | | -15 | 22 | -15+22=7 |
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 
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Answer:
So  factors to .
In other words,  .
Note: you can check the answer by expanding to get or by graphing the original expression and the answer (the two graphs should be identical).
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If not use quadratic formula
| 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=1369 is greater than zero. That means that there are two solutions:  .
Quadratic expression  can be factored:
Again, the answer is: 15, -22.
Here's your graph:
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