Question

5^2 = 2x^2 + (x+1)^2

Answer 1

$\large\boxed{\begin{array}{l}\sf 5^2=2x^2+(x+1)^2\\\sf 2x^2+x^2+2x+1=25\\\sf 3x^2+2x+1-25=0\\\sf 3x^2+2x-24=0\\\sf\Delta=b^2-4ac\\\sf\Delta=2^2-4\cdot3\cdot(-24)\\\sf\Delta=4+288\\\sf\Delta=292\\\sf x=\dfrac{-b\pm\sqrt{\Delta}}{2a}\\\\\sf x=\dfrac{-2\pm\sqrt{292}}{2\cdot3}\\\\\sf x=\dfrac{-2\pm2\sqrt{73}}{6}\\\\\sf x=\dfrac{-1\pm\sqrt{73}}{3}\begin{cases}\sf x_1=\dfrac{-1+\sqrt{73}}{3}\\\\\sf x_2=\dfrac{-1-\sqrt{73}}{3}\end{cases}\end{array}}$