$x^2-7x+2012=0$
$⇔(x^2-\frac{7}{2}x)-(\frac{7}{2}x-\frac{49}{4})+\frac{7999}{4}=0$
$⇔x(x-\frac{7}{2})-\frac{7}{2}(x-\frac{7}{2})+\frac{7999}{4}=0$
$⇔(x-\frac{7}{2})(x-\frac{7}{2})+\frac{7999}{4}=0$
$⇔(x-\frac{7}{2})^2+\frac{7999}{4}=0$
Vì $(x-\frac{7}{2})^2≥0∀x$ nên $(x-\frac{7}{2})^2+\frac{7999}{4}>0∀x$
Vậy P vô nghiệm.