Question 23327
{{{x^2 + 25 < 10x}}}


Begin by subtracting 10x from each side:
{{{x^2 -10x + 25 <0}}}


Can you see that this is a perfect square trinomial???

This just happens to factor, so you can write it {{{(x-5)^2 <0}}}, and a square of a real number can NEVER be less than zero, so this is NO SOLUTION.


You can also draw the graph of this {{{y= x^2 -10x +25 }}}.  Do you have a graphing calculator?  We do in algebra.com.  All you have to do is just type it in as a graph, and this is what comes out.

{{{graph(500,500, -10,10,-10,10, x^2 -10x+25 )}}}


Now, to answer the question from the graph, because the problem says {{{x^2 -10x +25<0 }}}, you need to find all the values of x on this graph where where the graph is BELOW the x-axis.  As you can see from the graph it is ALWAYS ABOVE THE X-axis, and it is NEVER BELOW the x=axis. 


You mentioned that you need graphing help.  Can you be more specific?  As I asked earlier, do you have a graphing calculator?  Do you know how to use algebra.com format to draw a graph as I did above?  If not, then just click on a problem here that has already been done that shows a graph (like this one!!), and look for "Show Source".  If you click on "Show Source" for this problem, you will see exactly what I typed in to get this problem posted as I did.  To get a graph, just type in three open set braces like this symbol: "{", followed by the word "graph" with an open parentheses, then all these numbers that set off the size of the graph, the x values, the y values, and then the equation for y, followed by closed parentheses and three closed set braces.  Try it sometime.  It works on the tutor end, and I think it can be used on the student side as well if you learned how to do it.


Or just get yourself a graphing calculator.  We use the TI 83+ and TI 84, so that is what I know the best, and I have a nice handout for it too.  Unfortunately, it is Texas Instruments who makes all the money on this, and not me!!  Have a good day.


R^2 at SCC