Answer
{$3,4$}
Work Step by Step
Step 1: Comparing $x^{2}-7x+12=0$ to the standard form of a quadratic equation $ax^{2}+bx+c=0$;
$a=1$, $b=-7$ and $c=12$
Step 2: The quadratic formula is:
$x=\frac{-b \pm \sqrt (b^{2}-4ac)}{2a}$
Step 3: Substituting the values of a,b and c in the formula:
$x=\frac{-(-7) \pm \sqrt ((-7)^{2}-4(1)(12))}{2(1)}$
Step 4: $x=\frac{7 \pm \sqrt (49-48)}{2}$
Step 5: $x=\frac{7 \pm \sqrt (1)}{2}$
Step 6: $x=\frac{7 \pm1}{2}$
Step 7: $x=\frac{7+1}{2}$ or $x=\frac{7-1}{2}$
Step 8: $x=\frac{8}{2}$ or $x=\frac{6}{2}$
Step 9: $x=4$ or $x=3$
Step 10: Therefore, the solution set is {$3,4$}.
