Answer
{$5\pm\sqrt 7$}
Work Step by Step
Step 1: Comparing $x^{2}-10x+18=0$ to the standard form of a quadratic equation $ax^{2}+bx+c=0$;
$a=1$, $b=-10$ and $c=18$
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:
$x=\frac{-(-10) \pm \sqrt ((-10)^{2}-4(1)(18))}{2(1)}$
Step 4: $x=\frac{10 \pm \sqrt (100-72)}{2}$
Step 5: $x=\frac{10 \pm \sqrt (28)}{2}$
Step 6: $x=\frac{10 \pm \sqrt (4\times7)}{2}$
Step 7: $x=\frac{10 \pm2\sqrt 7}{2}$
Step 8: $x=\frac{2(5 \pm\sqrt 7)}{2}$
Step 9: $x=5\pm\sqrt 7$
Step 10: $x=5+\sqrt 7$ or $x=5-\sqrt 7$
Step 11: Therefore, the solution set is {$5\pm\sqrt 7$}.
