Solve {l}{14.75=v_2^2-v_1^2}{35.316=v_3^2-v_1^2}{1.2v_{1}=0.45v_{2}+0.07v_{3}}

$$\left. \begin{array} { l } { 14.75 = v _ { 2 } ^ { 2 } - v _ { 1 } ^ { 2 } } \\ { 35.316 = v _ { 3 } ^ { 2 } - v _ { 1 } ^ { 2 } } \\ { 1.2 v _ { 1 } = 0.45 v _ { 2 } + 0.07 v _ { 3 } } \end{array} \right.$$

Solve for v_2, v_1, v_3

$$v_{2}=-\frac{\sqrt{3898647519054990410-2013736504500\sqrt{21365514881}}}{473541800}\approx -4.009148919\text{, }v_{1}=-\frac{9\sqrt{7297289295471610-24860944500\sqrt{21365514881}}}{473541800}\approx -1.150336932\text{, }v_{3}=\frac{9\sqrt{4202669197714730-994437780\sqrt{21365514881}}}{94708360}\approx 6.053038498$$

$$v_{2}=-\frac{\sqrt{2013736504500\sqrt{21365514881}+3898647519054990410}}{473541800}\approx -4.324180526\text{, }v_{1}=-\frac{9\sqrt{24860944500\sqrt{21365514881}+7297289295471610}}{473541800}\approx -1.987092655\text{, }v_{3}=-\frac{9\sqrt{994437780\sqrt{21365514881}+4202669197714730}}{94708360}\approx -6.266142132$$

$$v_{2}=\frac{\sqrt{2013736504500\sqrt{21365514881}+3898647519054990410}}{473541800}\approx 4.324180526\text{, }v_{1}=\frac{9\sqrt{24860944500\sqrt{21365514881}+7297289295471610}}{473541800}\approx 1.987092655\text{, }v_{3}=\frac{9\sqrt{994437780\sqrt{21365514881}+4202669197714730}}{94708360}\approx 6.266142132$$

$$v_{2}=\frac{\sqrt{3898647519054990410-2013736504500\sqrt{21365514881}}}{473541800}\approx 4.009148919\text{, }v_{1}=\frac{9\sqrt{7297289295471610-24860944500\sqrt{21365514881}}}{473541800}\approx 1.150336932\text{, }v_{3}=-\frac{9\sqrt{4202669197714730-994437780\sqrt{21365514881}}}{94708360}\approx -6.053038498$$