How do you solve s23(s+2)=4 ?

2 Answers
May 9, 2018

s=2ands=5

Explanation:

First, use the distributive property to simplify 3(s+2):

(3s)(32)

3s6

So now the equation is:
s23s6=4

Subtract 4 from both sides to get one side to equal to 0:
s23s6    4=4    4

s23s10=0

This equation is now in standard form, or ax2+bx+c=0.

To factor and solve for s, we need two numbers that:
1. Multiply up to ac=1(10)=10
2. Add up to b=3

The two numbers that do that are 2 and 5:
1.    25=10
2.    25=3

Therefore, we put it in factored form, or:
(s2)(s+5)=0

Since they multiply up to 0, we can do:
s2=0ands+5=0
       s=2and        s=5

Hope this helps!

May 9, 2018

Warning: Long answer, but hopefully worth it

s = -2 or 5

Explanation:

Following PEMDAS:

s23(s+2)=4

First, let's distribute -3 to s and +2. Remember that distributing means you're multiplying -3 by both terms in the parentheses. You should now have:

s23s6=4

Now, because you have no like terms, add six to both sides. You should now have:

s23s=10

This a quadratics equation, and you need to set the equation to 0 in order to solve it. So, subtract 10 from both sides. You should now have:

s23s10=0

Now, use the XBOX method. First, we need to multiply our first term by our last term (s210). We need then get 10s2.

Now, you have to multiply 2 numbers that get you 10s2 but also add to 3s. To do this, factor out 10:

1 - 10
2 - 5

-5 and 2 multiply to get you -10, and add to -3, so these are the terms we want to use. You should now have:

#s^2 -5s + 2s - 10 = 0

Now, make a table like this:

                           ?                  ?
                     ?  #s^2#          -5s

                   ?    2s                  -10

See where the question marks are? You want to find out what multiplies to give you the terms, starting with s2:

ss=s2, so these two will be s:

                            s                    ?
                     s  #s^2#          -5s

                   ?    2s                  -10

Now, you have two question marks remaining. Since you have s and ? that multiplies to -5s, the ? will be -5 because s * -5 = -5s. Add that in:

                            s                    -5
                     s  #s^2#          -5s

                   ?    2s                  -10

Now, we have one variable left. s * ? = 2s and -5 * ? equals -10. ? will be 2 because s * 2 = 2s and -5 * 2 = -10. So, insert your final variable:

                           s                    -5
                     s  #s^2#          -5s

                   2  2s                  -10

Now, your equation looks like this: (s + 2)(s - 5) = 0
Isolate each ordered pair and set it to 0 to find out what is s.

(s + 2) = 0; s = -2
(s - 5) = 0; s = 5

Source and for more info: