Question

What are the two solutions of 2x2 = –x2 – 5x – 1?

Answer 1

Answer:

The answer is

$x = \frac{ - 5 + \sqrt{13} }{6} \: \: \: \: or \: \: \: x = \frac{ - 5 - \sqrt{13} }{6}$

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

$x = \frac{ - b\pm \sqrt{ {b}^{2} - 4ac} }{2a}$

From the question

a = 3 , b = 5 , c = 1

So we have

$x = \frac{ - 5\pm \sqrt{ {5}^{2} - 4(3)(1) }}{2(3)} \\ = \frac{ - 5\pm \sqrt{25 - 12} }{6} \\ = \frac{ - 5\pm \sqrt{13} }{6}$

We have the final answer as

$x = \frac{ - 5 + \sqrt{13} }{6} \: \: \: \: or \: \: \: x = \frac{ - 5 - \sqrt{13} }{6}$

Hope this helps you