ANSWER
x=-1.2 or x=1.6
EXPLANATION
The given equation is:
[tex] 5{x}^{2} - 2x - 10 = 0[/tex] Group and combine the constant terms:
[tex]5{x}^{2} - 2x = 10 [/tex]
Divide through by 5
[tex]{x}^{2} - \frac{2}{5} x = 2[/tex]
Add the square of the coefficient of x to both sides:
[tex]{x}^{2} - \frac{2}{5} x + \frac{1}{25} = 2 + \frac{1}{25} [/tex]
The left hand side is now a perfect square
[tex]( {x - \frac{1}{5} })^{2} = \frac{51}{25} [/tex]
Take square root:
[tex]{x - \frac{1}{5} }=\pm \sqrt{\frac{51}{25}} [/tex]
[tex]{x = \frac{1}{5} }\pm \frac{ \sqrt{51} }{5}[/tex]
[tex]{x = \frac{1}{5} } - \frac{ \sqrt{51} }{5} \: or \: \: {x = \frac{1}{5} } + \frac{ \sqrt{51} }{5}[/tex]
x=-1.2 or x=1.6
