Question 192814
Let n = the integer in question, then, from the problem description you can write:
{{{n+n^2 = 132}}} Rearrange into a quadratic equation in standard form:
{{{n^2+n-132 = 0}}} Factor this.
{{{(n-11)(n+12) = 0}}} Apply the zero product rule.
{{{n-11 = 0}}} or {{{n+12 = 0}}} so that...
{{{n = 11}}} or {{{n = -12}}}:
 There are two solutions, one positive, (11) and one negative, (-12).
Check:
{{{n+n^2 = 132}}} Substitute n = 11.
{{{11+ 121 = 132}}}
{{{132 = 132}}} OK
{{{n+n^2 = 132}}} Substitute n = -12.
{{{-12+144 = 132}}}
{{{132 = 132}}} OK