f(x)=x^2+12x+32=0, solve for x

Method 1: Quadratic formulaf(x)= ax²+bx+c, therefore a=1, b=12, c=32 - quadratic formula= (-b+/-(b²-4ac)^1/2)/2ax=(-12+(144-128)^1/2/2 = -4 or x=(-12-(144-128)^1/2)/2 = -8
Method 2: FactoriseWe need to find a pair of numbers that when added make 12 and when multiplied make 32, 8 and 4 are our numbersTherefore f(x) can be written as (x+8)(x+4)The solutions to x are the numbers that make either bracket equal to 0, therefore x=-8 or x=-4