Solve the inequality and express in interval notation x^2 + 8x + 5 < 0

Hello from MrBillDoesMath!

x > -4 - sqrt(11) and x < -4 + sqrt(11)

Discussion:

Let's complete the square by adding and subtracting the value 16 from both sides

x^2 + 8x + 5 < 0   =>

(x^2 + 8x + 16) + 5 < 0 + 16 =>      complete the square

(x + 4) ^2 + 5  < 16 =>                    subtract 5 from both sides

(x+4)^2 < 16 - 5 = 11  =>                  take square root of both sides

(x+4) > -sqrt(11)  and ( x+4 ) < sqrt(11)  =>

x > -4 - sqrt(11) and x < -4 + sqrt(11)

Thank you,

MrB

hope this !

step-by-step explanation:

d = distance between moon and sun, which in this problem is the hypotenuse of a right triangle.  

the distance y is the side opposite to angle x in the right triangle.   use the definition of the sine function from basic trigonometry.

sin(x) = y/d ⇒

d = y/sin(x)