\text{Therefore:} && x^2+(x+5)^2& =(2x+1)^2\\\text{Eliminate the parentheses:} && x^2+x^2+10x+25& =4x^2+4x+1\\\text{Move all terms to the right hand side of the equation:} && 0& =2x^2-6x-24\\\text{Divide all terms by} \ 2: && 0& =x^2-3x-12\\\text{Solve using the quadratic formula:} && x& =\frac{3 \pm \sqrt{9+48}}{2}=\frac{3 \pm \sqrt{57}}{2}\\&& x& =\underline{\underline{5.27}} \ \text{or} \ x=-2.27