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You can put this solution on YOUR website!
First of all, you will certainly agree that a square has 4 sides, and that all 4 sides are equal in length. Also, if you are not already aware, the area of a square is all the space bounded by those 4 sides. The formula for the area is length times width, where the length is the size of a vertical side, while the width is the size of a horizontal side. However, since all sides are equal, the area is equal to the size of any side times itself(length squared, or width squared)\r
\n" ); document.write( "\n" ); document.write( "So, now we are given that some square has area x^2 +6x+9. What ever the length of a side is, when you multiply it by itself we should get x^2 +6x+9.\r
\n" ); document.write( "\n" ); document.write( "? * ? = x^2 +6x+9.\r
\n" ); document.write( "\n" ); document.write( "Now, directly taking the square root of a polynomial (such as x^2 +6x+9), is not necessarily obvious, or easy. So let's try to guess as wisely as we can.\r
\n" ); document.write( "\n" ); document.write( "( )*( ) = x^2 +6x+9
\n" ); document.write( "We need to fill the brackets and we have our answer, and note, whatever we do to one bracket, we must do to the other, since a square as equal sides, meaning the length and width have to be the same 'quantity.'\r
\n" ); document.write( "\n" ); document.write( "Let's start with x in the first bracket, immediately we get x in the second one, since we have to do the same to each bracket.\r
\n" ); document.write( "\n" ); document.write( "(x )*(x ) = x^2 +6x+9. We choose x, since x*x=x^2, so at least we get our first term. Now we notice the last term is 9, and that 9 is 3^2., so let's put a +3 in each bracket since 3*3=9. Doing this guarantees our last term, but there's going to be a middle term, let's hope it turns out to be 6x!
\n" ); document.write( "now we want to check what (x+3)*(x+3) actually expands into. If you are not familiar with these expansions, here's a general example that should explain it well enough to understand and solve this problem. If we have some (a+b)*(c+d), where a,b,c,d can be variables, or numbers, or anything really, then the expansion of (a+b)*(c+d) = (a*c)+(a*d)+(b*c)+(b*d); I believe this is known as the foil method.\r
\n" ); document.write( "\n" ); document.write( "Back to our problem, (x+3)*(x+3)=x^2+3x+3x+9 according to the formula. The two middle terms 3x, 3x can be added up since they are 'like' terms. 3x+3x = 6. \r
\n" ); document.write( "\n" ); document.write( "Therefore, (x+3)*(x+3) = x^2 +6x+9 meaning the length of side is x+3 units.\r
\n" ); document.write( "\n" ); document.write( "For the graph, along the x axis (y=0), plot some point and label that point (x,0). Then, from that labeled points, move 3 \"units\"(which can be cm, or whatever scale you are using), to the right and plot that point as (x+3,0). Then from the (x,0) point move 3 units up, and label that (x,3). Finally plot and label a point at (x+3,3)(I'll leave it to you to figure out how to find where this last point is on the graph). Once you have the 4 points, connect them, and that's a graph of the square. \n" ); document.write( "