Answer:
The answer is
[tex]x = \frac{ - 5 + \sqrt{13} }{6} \: \: \: \: or \: \: \: x = \frac{ - 5 - \sqrt{13} }{6} [/tex]
Step-by-step explanation:
2x² = - x² - 5x - 1
Rearrange the terms and simplify
That's
2x² + x² + 5x + 1 = 0
3x² + 5x + 1 = 0
Using the quadratic formula solve the equation
That's
[tex]x = \frac{ - b\pm \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]
From the question
a = 3 , b = 5 , c = 1
So we have
[tex]x = \frac{ - 5\pm \sqrt{ {5}^{2} - 4(3)(1) }}{2(3)} \\ = \frac{ - 5\pm \sqrt{25 - 12} }{6} \\ = \frac{ - 5\pm \sqrt{13} }{6} [/tex]
We have the final answer as
[tex]x = \frac{ - 5 + \sqrt{13} }{6} \: \: \: \: or \: \: \: x = \frac{ - 5 - \sqrt{13} }{6} [/tex]
Hope this helps you
