SOLUTION: Solve for w by factoring. w^2 � 4w � 5 = 0

Question 689931: Solve for w by factoring.
w^2 � 4w � 5 = 0
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!

Solved by pluggable solver: Factoring Quadratics with a leading coefficient of 1 (a=1)

In order to factor , first we need to ask ourselves: What two numbers multiply to -5 and add to -4? Lets find out by listing all of the possible factors of -5

Factors:

1,5,

-1,-5,List the negative factors as well. This will allow us to find all possible combinations

These factors pair up to multiply to -5.

(-1)*(5)=-5

Now which of these pairs add to -4? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -4

||

First Number	\|	Second Number	\|	Sum
1	\|	-5	\|	1+(-5)=-4
-1	\|	5	\|	(-1)+5=4

We can see from the table that 1 and -5 add to -4.So the two numbers that multiply to -5 and add to -4 are: 1 and -5 Now we substitute these numbers into a and b of the general equation of a product of linear factors which is: substitute a=1 and b=-5 So the equation becomes: (x+1)(x-5) Notice that if we foil (x+1)(x-5) we get the quadratic again

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