[tex] {(x + 2)}^{2} + {x}^{2} = (2x + 1) + (x + 3) - 3x + 1[/tex]
[tex] {x}^{2} + 4x + 4 + {x}^{2} = 2x + 1 + x + 3 - 3x + 1[/tex]
[tex] {x}^{2} + {x}^{2} + 4x - 2x - x + 3x = 1 + 3 + 1 - 4[/tex]
[tex]2 {x}^{2} + 4x = 1[/tex]
[tex]2 {x}^{2} + 4x - 1 = 0[/tex]
[tex]a = 2[/tex]
[tex]b = 4[/tex]
[tex]c = - 1[/tex]
[tex]\Delta = {b}^{2} - 4ac[/tex]
[tex]\Delta = {4}^{2} - 4 \times 2 \times ( - 1)[/tex]
[tex]\Delta = 16 + 8[/tex]
[tex]\Delta = 24[/tex]
[tex]x_{1,2}=\frac{-b\pm\sqrt{\Delta}}{2a}[/tex]
[tex]x_{1,2}=\frac{-4\pm\sqrt{24}}{2 \times 2}[/tex]
[tex]x_{1,2}=\frac{-4\pm2\sqrt{6}}{4}[/tex]
[tex]x_{1}=\frac{-4 + 2\sqrt{6}}{4} = \frac{2( - 2 + \sqrt{6} )}{4} = \frac{ - 2 + \sqrt{6} }{2} [/tex]
[tex]x_{2}=\frac{ - 4 - 2\sqrt{6}}{4} = \frac{2( - 2 - \sqrt{6} )}{4} = \frac{ - 2 - \sqrt{6} }{2} [/tex]
