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

#### toodumbformath

##### New member
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

Last edited by a moderator:

#### Subhotosh Khan

##### Super Moderator
Staff member
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

##### Elite Member
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.