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[tex]x^2+x^2=(x+2)^2\\\\2x^2=x^2+2\cdot x\cdot2+2^2\\\\2x^2=x^2+4x+4\\\\2x^2-x^2-4x-4=0\\\\x^2-4x-4=0\\\\a=1, \ b=-4,c=-4\\\\\Delta=b^2-4ac\rightarrow(-4)^2-4\cdot1\cdot(-4)=16+16=32\\\\\sqrt{\Delta}=\sqrt{32}=\sqrt{16\cdot2}=4\sqrt2\\\\x_1=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt2}{2}=\frac{4-4\sqrt2}{2}=2-2\sqrt2<0\\\\x_2=\frac{-b+\sqrt{\Delta}}{2a}\rightarrow\frac{-(-4)+4\sqrt2}{2}=\frac{4+4\sqrt2}{2}=\boxed{2+2\sqrt2}[/tex]
Odp. Długość boku wynosi 2 + 2√2.
