Question

Use the zero product property to find the solutions to the equation 2x^2-x-15=x(x+1).

Answer 1

hello :
2x²-x-15=x(x+1)
2x²-x-15-x(x+1) =0
2x²-x-15-x²-x =0
x²-2x-15 = 0
(x²-2x+1)-1-15 = 0
(x-1)² -4² =0
Use the zero product property and identity :a²-b²=(a-b)(a+b)
(x-1-4)(x-1+4) = 0
(x-5)(x+3) =0
x-5=0 or x+3 =0
x=5 or x= -3