bluebook math problem help!

<p>So I'm taking practice test 4 in the bluebook second edition,
and I just do not understand number 16 in section 6.
Here's the original question:</p>

<p>Let the function h be defined by h(x)=14+(x^2)/4.
If h(2m)=9m, what is one possible value of m?</p>

<p>So this seemed easy enough, I did the following plugging in:</p>

<p>9m=14+(2m^2)/4
0=.5m^2 -9m+14</p>

<p>and cannot factor from there. Obviously I'm plugging in wrong somewhere
or approaching the problem the wrong way.</p>

<p>the collegeboard site explanation is:</p>

<p>When 2m is substituted for x in function h, you get
(2m^2)/4=14+m^2. Since h(2m)=9m, it follows that
14+m^2=9m, or m^2-9m+14=0. </p>

<p>Obviously from there I understand it can factor to m=2 or m=7,
but I'm having trouble how they originally get (2m^2)/4=14+m^2.</p>

<p>I'm sorry if this is confusing!!
But if anyone could try and explain it to me that would be
greattttt.</p>

<p>Thanks so much
:)</p>

<p>When you plug 2m into 14 + x²/4, the entire 2m expression gets squared. In other words, you end up with (2m)²/4 = 4m²/4, not 2m²/4. From there:</p>

<p>14 + 4m²/4 = 9m simplifies to
14 + m² - 9m = 0, and you factor to get the answer. Hope that helps!</p>

<p>oh my gosh im an idiot.
THANK YOU SO MUCH :)))</p>