Question

completing the square

Answer 1

\[-4v^2 - 21v + 63 = -5v^2 \]
\[v^2 - 21v + 63 = 0 \]
\[v^2 - 21v + (-21/2)^2 = -63 + (-21/2)^2\]

Answer 2

\[v^2 - 21v + 63 = 0\]
\[\left( v - \dfrac{21}{2} \right)^2 - \left(\dfrac{21}{2}\right)^2+ 63 = 0\]
\[\left( v - \dfrac{21}{2} \right)^2 = \left(\dfrac{21}{2}\right)^2- 63 = 0\]
etc

Answer 3

typo\[\left( v - \dfrac{21}{2} \right)^2 = \left(\dfrac{21}{2}\right)^2- 63\qquad \color{red} { = 0} => \quad \text{typo}\]