solve |x^2-5|=5x+9

please explain step by step how to get to the answer

1 answer

x^2-5 = 5x+9 OR x^2-5 = -5x-9

first case:
x^2 - 5x - 14 = 0
(x-7)(x+2) 0
x = 7 or x = -2

case 2
x^2+5x+4 = 0
(x+1)(x+4)=0
x = -1 or -4

BUT, by definition, 5x+9≥0
x ≥ -9/5 or x ≥ -1.8

which leaves us with
x = 7 or x = -1