Solve the inequality (enter your answer using interval notation)

Question

2x^2 + 4x <0

Answer 1

2x² + 4x < 0

2x(x + 2) < 0

The two factors must be of different sign

x < 0 and x + 2 > 0

x < 0 and x > -2

or

x > 0 and x + 2 < 0

x > 0 and x < -2

Not possible

{x | -2 < x < 0}

Answer 2

2x^2+4x=0

divide by 2

x^2+2x=0/2=0

complete the square

add (2/2)^2 =1^2=1 to both sides

x^2+2x+1=0+1

(x+1)^2=1

take the square root of both sides

x+1 = +/-1

x=-1+/-1 =0 or -2

0 and -2 are the upper & lower bounds

x>-2 and x<0

x is in the interval (-2,0)