Answer:
x = -1 ± √6
Step-by-step explanation:
[tex]x^{2} +2x - 5 = 0[/tex]
Lets use the quadratic formula → [tex]x = \frac{-b + \sqrt{b^{2} - 4ac} }{2a} \:or \frac{-b - \sqrt{b^{2}- 4ac } }{2a}[/tex]
So ,
[tex]x = \frac{(-2) + \sqrt{(2)^{2} - (4\times1\times-5) } }{2\times1} \:or \frac{(-2) - \sqrt{(2)^{2} - (4\times1\times-5) }}{2\times1}[/tex]
[tex]=> x = \frac{-2 + \sqrt{24} }{2} \:or \frac{-2-\sqrt{24} }{2}[/tex]
[tex]=> x = \frac{-2 + 2\sqrt{6} }{2} \:or \frac{-2 - 2\sqrt{6} }{2}[/tex]
Lets take 2 common from numerator.
[tex]=> x = \frac{2(-1 + \sqrt{6}) }{2} \:or \frac{2(-1-\sqrt{6}) }{2}[/tex]
Cancelling 2 from numerator & denominator gives
[tex]x = (-1+\sqrt{6} ) \: or (-1 - \sqrt{6} )[/tex]
