Have to solve x^2 + 2x + 8 = 0; answer should be R

[toodumbformath]

^​sorry english is not my first language im not sure what category to put it in.

I have to solve x² + 2x + 8 = 0
answer should be R but i dont know to to solve it step by step.
if i use abc formula then i get negative number under the squareroot.

thanks for help

 

[Deleted member 4993]

^​sorry english is not my first language im not sure what category to put it in.

I have to solve x² + 2x + 8 = 0
answer should be R but i dont know to to solve it step by step.
if i use abc formula then i get negative number under the squareroot.

thanks for help

You are correct.

As posted, the given equation has "complex" solutions.

 

[HallsofIvy]

Completing the square, \(\displaystyle x^2+ 2x+ 8= x^2+ 2x+ 1- 1+ 8= (x+ 1)^2+ 7\). A square of a real number is never negative so \(\displaystyle (x+ 1)^2+ 7\) is never less than 7 and, in particular, never 0. This equation has no solution in the real numbers.

If we allow complex numbers then we can say \(\displaystyle (x+ 1)^2= -7\) so \(\displaystyle x+ 1= \pm i\sqrt{7}\) so that the complex numbers \(\displaystyle -1+ i\sqrt{7}\) and \(\displaystyle -1- i\sqrt{7}\) satisfy the equation.