Question

Solve for x Xsquare+ 4x+45=0

Answer 1

For this case we must solve the following quadratic equation:

$x ^ 2 + 4x + 45 = 0$

Where:

$a = 1\\b = 4\\c = 45$

The solution will be given by:

$x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2a}$

Substituting the values we have:

$x = \frac {-4 \pm \sqrt {4 ^ 2-4 (1) (45)}} {2 (1)}\\x = \frac {-4 \pm \sqrt {16-180}} {2}\\x = \frac {-4 \pm \sqrt {-164}} {2}$

By definition we have to:

$i ^ 2 = -1$

So:

$x = \frac {-4 \pm \sqrt {164i ^ 2}} {2}\\x = \frac {-4 \pm i \sqrt {164}} {2}\\x = \frac {-4 \pm i \sqrt {2 ^ 2 * 41}} {2}\\x = \frac {-4 \pm2i \sqrt {41}} {2}\\x = -2 \pm i \sqrt {41}$

Thus, we have two complex roots:

$x_ {1} = - 2 + i \sqrt {41}\\x_ {2} = - 2-i \sqrt {41}$

Answer:

$x_ {1} = - 2 + i \sqrt {41}\\x_ {2} = - 2-i \sqrt {41}$