Answer:
x=-0.37 or 5.37
Step-by-step explanation:
The quadratic formula is;
[tex]x = \frac{ - b\pm \sqrt{ {b}^{2} - 4ac } }{2a} [/tex]
The expression to be solved is
[tex] {x}^{2} - 5x - 2 = 0[/tex]
Comparing this to the general form of the quadratic equation,
[tex] a{x}^{2} + bx + c = 0 [/tex]
a=1, b=-5 and c =-2.
We substitute these values into the quadratic formula
[tex] \implies x = \frac{ - ( - 5)\pm \sqrt{ { (- 5)}^{2} - 4(1)( - 2)} }{2(1)} [/tex]
Simplifying we obtain,
[tex] x = \frac{ 5\pm \sqrt{25 + 8}}{2} [/tex]
[tex] \implies x = \frac{ 5\pm \sqrt{28}}{2} [/tex]
[tex] \implies x = \frac{5 + 2\sqrt{7} }{2}or \frac{5 - 2 \sqrt{7} }{2} [/tex]
[tex]\implies x = \frac{5}{2} + \sqrt{7} or \frac{5 }{2} - \sqrt{7} [/tex]
x=5.37 or -0.37
