What is w^2+5w=24 I dont even know where to begin?

Question

What is w^2+5w=24 I dont even know where to begin?

Answer 1

w^2 +5w -24=0

(w+8)(w-3)=0

w= - 8 or w =3

Answer 2

w^2 + 5w = 24

We want all of the terms on the same side of the equal sign to form a quadratic equation.

First subtract 24 from both sides

w^2 + 5w - 24 = 24 - 24

w^2 + 5w - 24 = 0

The first step to factor this is to set up the parentheses.

( ) * ( ) = 0

Since the coeficient of the first term is 1, then we just take the square root of w^2 to obtain the first term for our factor.

(w  ) * (w  )

Next, we know the product of the second terms in the factor = -24. So that means one of them must be positive and the other negative to have a negative product.

So now we have

(w +  ) * (w -   )

We also know that the sum of the cross mulitplied FOIL terms must be +5

And since the product of these last terms in each factor = -24, the only possible combinations include:

8 * 3

6 * 4

12 * 2

If we test those three possible combinations, we find only one will work. Therefore

w^2 + 5w - 24 = 0

(w + 8) * (w - 3) = 0

In order to satisfy that equation, since the product of the two factors must = 0, then one or both of them must = 0

For w + 8 = 0

w = -8

For w - 3 = 0

w = +3