What are the y values when f(x)=g(x)?

Question

f(x) = -x⁴-3x²+6

g(x) = 2|x+2|

Answer 1

|x+2| = (-x^4-3x^2 +6)/2

x= -x^4/2-3x^2/2-5

x^4/2+3x^2/2 +x+5=0

x^4 +3x^2+2x+10=0 no positive real solutions

2 possible negative real solutions, 2 or 4 imaginary solutions

looks like no real solutions, maybe graph it to make sure there are no x intercepts, the curve looks entirely above the x axis

also check

-x-5 = (-x^4-3x^2+6)/2

x^4+3x^2 -2x-16=0

1 possible real solution, 1 possible negative real solution, 2 or 4 imaginary

one negative solution is between 0 and -1

one positive solution is between 0 and 1

graph it, x intercepts are the 2 solutions

2 imaginary solutions

x=-1 or about .533

or graph the left side absolute value which is a V shape

and graph the right side a downward opening parabola

where they intersect is the solution 2 points, about -.1 and .533

y=0

(-1,0), (.533,0)