[tex]x^2-18=0\ \ \ |+18\\x^2=18 \ \textgreater \ 0\\\\x=\pm\sqrt{18}\\\\\boxed{Answer:\ 2}[/tex]
[tex]x^2+5x-10=0\\\\\underbrace{x^2+2x\cdot2.5+2.5^2}_{(a+b)^2=a^2+2ab+b^2}-2.5^2-10=0\\\\(x+2.5)^2-6.25-10=0\\\\(x+2.5)^2-16.25=0\ \ \ |+16.25\\\\(x+2.5)^2=16.26\to x+2.5=\pm\sqrt{16.25}\ \ \ |-2.5\\\\x=-\sqrt{16.25}-2.5\ \vee\ x=\sqrt{16.25}-2.5\\\\x\approx-6.53\ \vee\ x\approx1.53\\\\\boxed{Answer:\ 1.53,\ -6.53}[/tex]
[tex]h=-16t^2+vt+c\\\\v=116\ ft/s;\ c=101\ ft;\ h=0\\\\substitute:\\\\0=-16t^2+116t+101\\\\a=-16;\ b=116;\ c=101\\\\t_1=\dfrac{-116-\sqrt{116^2-4\cdot(-16)\cdot101}}{2\cdot(-16)}\approx8.035\approx8\\\\t_2=\dfrac{-116+\sqrt{116^2-4\cdot(-16)\cdot101}}{2\cdot(-16)}\approx-0.786 \ \textless \ 0\\\\\boxed{Answer:\ 0=-16t^2+116t+101;\ 8s}[/tex]
