Question 1190247
<br>
The words say<br>
{{{3x+x^2=108}}}<br>
That's a quadratic equation; get everything on one side and factor:<br>
{{{x^2+3x-108=0}}}<br>
With a negative constant term, the factorization has to be of the form (x+a)(x-b); so we need two numbers whose product is 108 and whose difference is 3 -- 12 and 9.<br>
{{{(x+12)(x-9)=0}}}
{{{x=-12}}} or {{{x=9}}}<br>
Check to see if both solutions to the equation are solutions to the original problem:
x=-12: 3x+x^2 = -36+144 = 108 check
x=9: 3x+x^2 = 27+81 = 108 check<br>
ANSWERS: -12 or 9<br>