# How do you solve s^2-3(s+2)=4 ?

May 9, 2018

$s = 2 \mathmr{and} s = - 5$

#### Explanation:

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

$\left(- 3 \cdot s\right) - \left(3 \cdot 2\right)$

$- 3 s - 6$

So now the equation is:
${s}^{2} - 3 s - 6 = 4$

Subtract $\textcolor{b l u e}{4}$ from both sides to get one side to equal to $0$:
${s}^{2} - 3 s - 6 \quad \textcolor{b l u e}{- \quad 4} = 4 \quad \textcolor{b l u e}{- \quad 4}$

${s}^{2} - 3 s - 10 = 0$

This equation is now in standard form, or $a {x}^{2} + b x + c = 0$.

To factor and solve for $s$, we need two numbers that:
$1.$ Multiply up to $a c = 1 \left(- 10\right) = - 10$
$2.$ Add up to $b = - 3$

The two numbers that do that are $\textcolor{b l u e}{2}$ and $\textcolor{b l u e}{- 5}$:
$1. \quad \quad 2 \cdot - 5 = - 10$
$2. \quad \quad 2 - 5 = - 3$

Therefore, we put it in factored form, or:
$\left(s - 2\right) \left(s + 5\right) = 0$

Since they multiply up to $0$, we can do:
$s - 2 = 0 \mathmr{and} s + 5 = 0$
$\quad \quad \quad$ $s = 2 \mathmr{and} \quad \quad \quad \quad s = - 5$

Hope this helps!

May 9, 2018

Warning: Long answer, but hopefully worth it

s = -2 or 5

#### Explanation:

Following PEMDAS:

${s}^{2} - 3 \left(s + 2\right) = 4$

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:

${s}^{2} - 3 s - 6 = 4$

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

${s}^{2} - 3 s = 10$

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:

${s}^{2} - 3 s - 10 = 0$

Now, use the XBOX method. First, we need to multiply our first term by our last term $\left({s}^{2} \cdot - 10\right)$. We need then get $- 10 {s}^{2}$.

Now, you have to multiply 2 numbers that get you $- 10 {s}^{2}$ but also add to $- 3 s$. 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 ${s}^{2}$:

$s \cdot s = {s}^{2}$, 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