Question

|x|=x^2+x-15 solve absolute value equation and show steps please

Answer 1

x=√15 or x = -5 or x=3

Explanation:

Possibility one:

x=x^2+x-15

x-x^2=x^2+x-15-x^2 (subtract x^2 from both sides)

-x^2+x=x-15

-x^2+x-x=x-15-x (subtract x from both sides)

-x^2=-15

-x^2/-1=-15/-1 (divide both sides by -1)

x^2=15

square root both sides

x=√15 or x=-√15

Possibility two:

x=(-x^2+x-15)

x=-x^2-x+15 (simplify)

x-(-x^2-x+15)=-x^2-x+15-(-x^2-x+15) (subtract both sides by -x^2-x+15)

x^2+2x-15=0

(x-3)(x+5)=0 (factor left side of equation)

x-3=0 or x+5=0 (set factors equal to 0)

x=3 or x=-5