Simplify \({6}^{2}\) to \(36\).
\[20=\frac{{V}^{2}-36}{2\times 1.6}\]
Rewrite \({V}^{2}-36\) in the form \({a}^{2}-{b}^{2}\), where \(a=V\) and \(b=6\).
\[20=\frac{{V}^{2}-{6}^{2}}{2\times 1.6}\]
Use Difference of Squares: \({a}^{2}-{b}^{2}=(a+b)(a-b)\).
\[20=\frac{(V+6)(V-6)}{2\times 1.6}\]
Simplify \(2\times 1.6\) to \(3.2\).
\[20=\frac{(V+6)(V-6)}{3.2}\]
Multiply both sides by \(3.2\).
\[64=(V+6)(V-6)\]
Expand.
\[64={V}^{2}-{6}^{2}\]
Simplify \({6}^{2}\) to \(36\).
\[64={V}^{2}-36\]
Add \(36\) to both sides.
\[64+36={V}^{2}\]
Simplify \(64+36\) to \(100\).
\[100={V}^{2}\]
Take the square root of both sides.
\[\pm \sqrt{100}=V\]
Since \(10\times 10=100\), the square root of \(100\) is \(10\).
\[\pm 10=V\]
Switch sides.
\[V=\pm 10\]
V=10,-10
