Answer:
[tex]x = \frac{2}{3} + \frac{\sqrt{10} }{3} , x = \frac{2}{3} - \frac{\sqrt{10} }{3}[/tex]
Step-by-step explanation:
Multiplying the coefficient of x by the constant to get:
3 x (-2) = -6
Find factors of -6 that equal the middle term -4.
Since, no such factors can be found so we can solve the equation by completing the square.
To complete the square, divide the equation by the coefficient of x^2 which is 3 to get:
[tex]x^{2} - \frac{4}{3} x - \frac{2}{3} = 0[/tex]
[tex]x^{2} - \frac{4}{3} x = \frac{2}{3}[/tex]
Now divide the coefficient of x by 2 and add the square of the result to both sides of the equation:
[tex]x^{2} - \frac{4}{3} x + (-\frac{2}{3} )^{2} = \frac{2}{3} + (-\frac{2}{3} )^{2}[/tex]
[tex](x - \frac{2}{3} )^2 = \frac{2}{3} + \frac{4}{9}[/tex]
[tex](x - \frac{2}{3} )^2 = \frac{4}{9}[/tex]
[tex]\sqrt{(x - \frac{2}{3} )^2} = \sqrt{\frac{4}{9} }[/tex]
[tex]x - \frac{2}{3} = \sqrt{\frac{10}{9} }[/tex] , [tex]x - \frac{2}{3} = -\sqrt{\frac{10}{9} }[/tex]
[tex]x = \frac{2}{3} + \frac{\sqrt{10} }{3} , x = \frac{2}{3} - \frac{\sqrt{10} }{3}[/tex]
