Question

X to the second power plus eight x plus 25 equal zero

Answer 1

For this case we must solve the following quadratic equation:

`x ^ 2 + 8x + 25 = 0`

We solve the equation using the quadratic formula:

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

Where:

`a = 1\\b = 8\\c = 25`

Substituting we have:

`x = \frac {-8 \pm \sqrt {8 ^ 2-4 (1) (25)}} {2 (1)}\\x = \frac {-8 \pm \sqrt {64-100}} {2}\\x = \frac {-8 \pm \sqrt {-36}} {2}`

By definition we have that
`i ^ 2 = -1`, then:

`x = \frac {-8 \pm \sqrt {36i ^ 2}} {2}\\x = \frac {-8 \pmi \sqrt {36}} {2}\\x = \frac {-8 ± 6i} {2}\\x = -4 \pm3i`

We have two complex roots:

`x_ {1} = - 4 + 3i\\x_ {2} = - 4-3i`

Answer:

`x_ {1} = - 4 + 3i\\x_ {2} = - 4-3i`