SOLUTION: I'm not sure if I belong here or not. To me, my problem seems like a geometry problem even though we're not studying that right now. Either way I can't figure it out. Would someone

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Question 443941: I'm not sure if I belong here or not. To me, my problem seems like a geometry problem even though we're not studying that right now. Either way I can't figure it out. Would someone be willing to help me please? The problem is:
A square has an area of 16x^2+56x+49. Find the length of the side.
Make a sketch of the square.
Found 4 solutions by rwm, chriswen, ankor@dixie-net.com, richard1234:
Answer by rwm(914) About Me  (Show Source):
You can put this solution on YOUR website!
It can't be factored so you either have to complete the square or use the quadratic formula
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 16x%5E2%2B56x%2B49+=+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=%2856%29%5E2-4%2A16%2A49=0.

Discriminant d=0 is zero! That means that there is only one solution: x+=+%28-%2856%29%29%2F2%5C16.
Expression can be factored: 16x%5E2%2B56x%2B49+=+16%28x--1.75%29%2A%28x--1.75%29

Again, the answer is: -1.75, -1.75. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+16%2Ax%5E2%2B56%2Ax%2B49+%29

Answer by chriswen(106) About Me  (Show Source):
You can put this solution on YOUR website!
16x^2+56x+49 sub into %28a%2Bb%29%5E2=a%5E2%2B2ab%2Bb%5E2
(4x)^2+(2)*(4)*(7)+(7)^2
=(4x+7)^2
So therefore the square is (4x+7)*(4x+7). So therefore one side of the square is 4x+7.
I'll try to make a sketch. (dots are filler)
...
....4x + 7
. . ____ ____
4x[16x^2[..28x..[
. .[____[____[
. .[ ..28x..[ ..49..[
+7[____[____[
Does that make sense?
That is supposed to be a square, divided into four sections.
Both sides are 4x+7.
If you add up the area inside, you'll get what was in the question. I got the area in the subdivisions by l*w. 4x*4x=16x^2 ... 4x*7=28 ... 7*7=49

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A square has an area of 16x^2+56x+49.
I think this should be 16x^2-56x+49, otherwise you get a neg solution
:
Find the length of the side.
:
Note that in this expression, the 16 and 49 are perfect squares, 4^2 & -7^2
the coefficient of x is the sum of (4*-7)+(4*-7) therefore
This can be factored as a perfect square
(4x-7)(4x-7) = 0
4x = 7
x = 7%2F4
x = 1.75 units, the side of the square

Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
It appears to be a geometry problem, but it is mostly an algebra problem. If the square's area is 16x^2 + 56x + 49, then

where a,b are constants, ax+b is the side length. The only "geometry" part is knowing the area of a square.

Since the x^2 coefficient is 16, a^2 = 16, so a = +/- 4. If a = 4, guess and check reveals b = 7. If a = -4, b = -7. Hence, the side length is either 4x + 7 or -4x - 7, whichever is positive.