1) [tex]k^2 + \frac{1}{2}k - \frac{5}{14} = 0
k^2 + \frac{1}{2}k + \frac{1}{16} = \frac{5}{14}+\frac{1}{16}
(k+\frac{1}{4})^2 = \frac{47}{112}
k+\frac{1}{4} = ±\sqrt{ \frac{47}{112}}
\boxed{k = ±\sqrt{ \frac{47}{112}} - \frac{1}{4}}[/tex]
2)[tex]x^2 -15x+10=0
x^2 -15x + \frac{225}{4} = \frac{225}{4} -10
(x- \frac{15}{2})^{2}=\frac{185}{4}
x- \frac{15}{2} = ±\sqrt{\frac{185}{4}}
\boxed{x = ±\frac{ \sqrt{185}+15}{2}}[/tex]
