Alg3.2.4

From Exampleproblems

Solve for $x\,$ : $5x^2+6x+1=0\,$

Multiplying the two extreme constants which is 5 and the factors for 5 are 5 and 1,which when we add becomes 6,also both are positive,

Hence,writing the middle term as a combination of these two factors,it looks like, $5x^2+5x+1x+1=0\,$

taking out the common terms in the first two terms and last two terms, $5x(x+1)+1(x+1)=0\,$

Now taking out the common in the above equation, $(x+1)(5x+1)=0\,$

Now either of the expression on the right equals to zero, $(x+1)=0\,$ or $(5x+1)=0\,$

The solution is $x=-1\,$ or $5x=-1\,$

Final solution is $x=-1\,$ or $x={-1/5}\,$