Given equation is x²+9x+18 = 0
➝ x²+9x = -18
➝ x²+2(9x)/2 = -18
➝ x²+2(x)(9/2) = -18
On adding (9/2)² both sides then
➝ x²+2(x)(9/2)+(9/2)² = -18+(9/2)²
➝ [x+(9/2)]² = -18+(81/4)
➝ [x+(9/2)]² = (-72+81)/4
➝ [x+(9/2)]² = 9/4
➝ x+(9/2) = ±√(9/4)
➝ x+(9/2) = ±3/2
➝ x = (±3/2) -(9/2)
➝ x = (3/2)-(9/2) or -(3/2)-(9/2)
➝ x = (3-9)/2 or (-3-9)/2
➝ x = -6/2 or -12/2
➝ x = -3 or -6
The roots are -3 and -6
or x²+6x+3x+18 = 0
➝ x(x+6)+3(x+6) = 0
➝ (x+6)(x+3) = 0
➝ x+6 = 0 or x+3 = 0
➝ x = -6 or x = -3