Answer:
[tex]x=2+-i \sqrt{6}[/tex]
Step-by-step explanation:
[tex]x^2 + 4x + 10[/tex]
To find out the solution we set the expression =0 and solve for x
[tex]x^2 + 4x + 10=0[/tex]
Apply quadratic formula to solve for x
[tex]x=\frac{-b+-\sqrt{b^2-4ac}}{2a}[/tex]
a=1, b=4, c=10 plug in the values in the formula
[tex]x=\frac{-4+-\sqrt{4^2-4(1)(10)}}{2a}[/tex]
[tex]x=\frac{-4+-\sqrt{-24}}{2(1)}[/tex]
The value of square root (-1) is 'i'
[tex]x=\frac{-4+-2i\sqrt{6}}{2}[/tex]
Divide each term by 2
[tex]x=2+-i\sqrt{6}[/tex]
