Solve {c}{a^2+b^2+c^2=1}{-a+2b+c=0}{-5a+3a+4c=frac{5sqrt{2}}{2}}

$$\left\{ \begin{array} { c } { a ^ { 2 } + b ^ { 2 } + c ^ { 2 } = 1 } \\ { - a + 2 b + c = 0 } \\ { - 5 a + 3 a + 4 c = \frac { 5 \sqrt { 2 } } { 2 } } \end{array} \right.$$

Solve for a, b, c

$$a=-\frac{5\sqrt{2}}{28}-\frac{2}{7}\approx -0.538252422\text{, }b=\frac{-5\sqrt{2}-1}{14}\approx -0.576504844\text{, }c=\frac{15\sqrt{2}}{28}-\frac{1}{7}\approx 0.614757266$$

$$a=-\frac{5\sqrt{2}}{28}+\frac{2}{7}\approx 0.03317615\text{, }b=\frac{1-5\sqrt{2}}{14}\approx -0.433647701\text{, }c=\frac{15\sqrt{2}}{28}+\frac{1}{7}\approx 0.900471551$$