Question

Solve for:" alt="x^{2} + 5x = 1" align="absmiddle" class="latex-formula">

Answer 1

$x^2+5x-1=0\\x^2+5x+(\frac{5}{2})^2-(\frac{5}{2})^2-1=0\\(x+\frac{5}{2})^2-\frac{25}{4}-\frac{4}{4}=0\\(x+\frac{5}{2})^2-\frac{29}{4}=0\\(x+\frac{5}{2})^2=\frac{29}{4}\\x+\frac{5}{2}=\sqrt{\frac{29}{4}} , x+\frac{5}{2}=-\sqrt{\frac{29}{4}}\\x=\frac{\sqrt{29} }{2} - \frac{5}{2} , x=-\frac{\sqrt{29} }{2} - \frac{5}{2} \\x=\frac{\sqrt{29}-5 }{2} , x=-\frac{\sqrt{29} -5}{2}$