Question

solve for:

$x^{2} + 5x = 1$

Answer 1

$x^2+5x-1=0\\

x^2+5x+(\frac{5}{2})^2-(\frac{5}{2})^2-1=0\\

(x+\frac{5}{2})^2-\frac{25}{4}-\frac{4}{4}=0\\

(x+\frac{5}{2})^2-\frac{29}{4}=0\\

(x+\frac{5}{2})^2=\frac{29}{4}\\

x+\frac{5}{2}=\sqrt{\frac{29}{4}} , x+\frac{5}{2}=-\sqrt{\frac{29}{4}}\\

x=\frac{\sqrt{29} }{2} - \frac{5}{2} , x=-\frac{\sqrt{29} }{2} - \frac{5}{2} \\

x=\frac{\sqrt{29}-5 }{2} , x=-\frac{\sqrt{29} -5}{2}$