Verified answer

[tex]\displaystyle\bf\\x^{2} +5x-2=0\\\\Teorema \ Vieta \ :\\\\x_{1} + x_{2} =-5\\\\x_{1}\cdot x_{2} =-2\\\\x_{1}^{2} +x_{2}^{2} =(x_{1}+ x_{2} )^{2} -2\cdot x_{1}\cdot x_{2} =(-5)^{2}-2\cdot(-2)=\\\\=25+4=29[/tex]