[tex]m^2+7m- \frac{51}{4}=0 [/tex]
[tex]m^2+7m= \frac{51}{4} [/tex]
[tex]m^2+7m+( \frac{7}{2})^2= \frac{51}{4}+ ( \frac{7}{2} )^2[/tex]
[tex]\sqrt{(m+ \frac{7}{2})^2 }= +or-\sqrt{ \frac{100}{4} }[/tex]
[tex]m+ \frac{7}{2}= +or- \frac{10}{2} [/tex]
[tex]m= \frac{10}{2}- \frac{7}{2} [/tex]
[tex]m= \frac{3}{2} [/tex]
[tex]m=- \frac{10}{2}- \frac{7}{2} [/tex]
[tex]m=- \frac{17}{2} [/tex]
Check:
[tex]m= \frac{3}{2} [/tex]
[tex]( \frac{3}{2})^2+7( \frac{3}{2})- \frac{51}{4}=0 [/tex]
[tex] \frac{9}{4}+ \frac{21}{2}- \frac{51}{4} =0[/tex]
[tex] \frac{51}{4} - \frac{51}{4}=0 [/tex]
[tex]0=0[/tex]
[tex]m= -\frac{17}{2} [/tex]
[tex]( -\frac{17}{2})^2+7( -\frac{17}{2})- \frac{51}{4}=0 [/tex]
[tex] \frac{289}{4}- \frac{119}{2}- \frac{51}{4}=0 [/tex]
[tex] \frac{51}{4}- \frac{51}{4} =0[/tex]
[tex]0=0[/tex]
[tex]w^2+6w-11=0[/tex]
[tex]w^2+6w=11[/tex]
[tex]w^2+6w+(3)^2=11+(3)^2[/tex]
[tex] \sqrt{(w+3)^2}= \sqrt{20} [/tex]
[tex]w+3=+or- \sqrt{20} [/tex]
[tex]w=+or- \sqrt{20}-3 [/tex]
[tex] \left \{ {{w= \sqrt{20}-3 } \atop {w= -\sqrt{20}-3 }} \right. [/tex]
(In checking you can just use a scientific calculator... Just substitute the variables with the given value...) ^_^ \/
