Verified answer

#1.

[tex] \sf {3x}^{2} - 9x + \underline{ \: \: \: \: \: } \implies {x}^{2} - \frac{9}{3} x + \bigg( \frac{ - 9}{2(3)} \bigg) {}^{2} \\ [/tex]

Then,

[tex]\sf = {x}^{2} - 3x + \frac{81}{36} \\ [/tex]

[tex]\sf = {x}^{2} - 3x + \frac{9}{4} \\ [/tex]

[tex] \: [/tex]

#2.

[tex] \sf {5x}^{2} - 10x+ \underline{ \: \: \: \: \: } \implies {x}^{2} - \frac{10}{5} x + \bigg( \frac{ - 10}{2(5)} \bigg) {}^{2} \\ [/tex]

Then,

[tex] \sf = {x}^{2} - 2x + \cancel{ \frac{100}{100} } \\ [/tex]

[tex] \sf = {x}^{2} - 2x + 1[/tex]

[tex] \: [/tex]

#3.

[tex] \sf {3x}^{2} + 5x + \underline{ \: \: \: \: \: } \implies {x}^{2} + \frac{5}{3} x + \bigg( \frac{5}{2(3)} \bigg) {}^{2} \\ [/tex]

Then,

[tex] \sf = {x}^{2} + \frac{5}{3} x + \frac{25}{36} \\ [/tex]

[tex] \: [/tex]

#4.

[tex] \sf2x {}^{2} + 8x + \underline{ \: \: \: \: \: } \implies {x}^{2} + \frac{8}{2} x + \bigg( \frac{8}{2(2)} \bigg) {}^{2} \\ [/tex]

Then,

[tex] \sf = {x}^{2} + 4x + \frac{81}{16} \\ [/tex]

[tex] \: [/tex]

#5.

[tex] \sf7x {}^{2} - x + \underline{ \: \: \: \: \: } \implies {x}^{2} + \frac{( - 1)}{7} x + \bigg( \frac{( - 1)}{2(7)} \bigg) {}^{2} \\ [/tex]

Then,

[tex] \sf = {x}^{2} - \frac{1}{7} x + \frac{1}{196} \\ [/tex]