## How Would You Solve the Equation: 3q² + 2q = 2q² - 2q + 45 (Difficult)

1. The first step of solving the equation is to get everything away from the right side.

Ex. (3q² + 2q = 2q² - 2q + 45)

a) Subtract 2q² from 3q² and getting q²

_3q² + 2q = 2q² - 2q + 45

-2q²

q² + 2q = 2q + 45

b) Next, add 2q to 2q , getting 4q

q² + 2q = -2q + 45

___ - 2q

q² + 4q = 45

c) Now, subtract 45, getting -45 at the END of the equation.

q² + 4q = 45

____-45

q² + 4q - 45 = 0

d) Your factored equation should be q² + 4q - 45 = 0

2. How to find the solutions of Quadratics

Ex. (q² + 4q - 45 = 0)

a) First step is to find 2 factors of -45 that have a sum of 4.

b) The 2 factors would be (9,-5)

c) Next, make 2 binomials

Ex. (q+9) (q-5) = 0

d) Once you have your 2 binomials, make both equations equal 0.

Ex. q+9=0 q-5=0

e) Solve the equations-

q + 9 = 0 (Subtract the 9 from both sides)

___- 9 q = - 9

q - 5 = 0 (Add 5 to both sides)

__+5 q = 5

f) Now you have found your solutions. (-9,5)

_______________________________________________________________________________________

**An easier way to find out what your solutions are...

1) When you find out the factors,

## How would you solve the equation: k² + 13k + 40 = 0 (medium)

a) The first step multiply k² and 40 which gets you 40

+ 13k + 40 = 0

b) The second step is to find the factors of 40 that equal 13 which is 8 and 5

__40|13

8+5 | 13

c) So then you take the 13 and split it into two parts (using the two factors):

k² + 13k + 40 = 0

k² + 8k + 5k + 40 = 0

d) Now here is the tricky part... split the equations into two parts:

k² + 8k | 5k + 40 = 0

e) Then you find the common factor in both equations as so:

k² + 8k

*Think about it what do they both have in common. They both have k and 1 as factored the same so...*

k(k + 8)

*Use distributive property on the first equation in order to check if your right*

k(k + 8) = k² + 8k = 0

f) Do the same thing to the other half of the equation:

5k + 40 = 0

*Find what they both have in common. They are both divisible by five.*

5(k + 8)

*Always makes sure to check*

5(k + 8) = 5k + 40 = 0

g) Then plug the equations back together again:

k(k + 8) + 5(k + 8)

*Take the (k + 8) and add them with the (k + 5)

h) Solve both (k + 8) and (k + 5)

k + 8 = 0

___-8__-8

k = -8

i) Solve

k + 5 = 0

__- 5__-5

k = -5

You are left with your solution set which is {-5, -8}

## How would solve the equation: (x - 2) (x + 6) = 0 (easy)

1. The first step is to set both of the equations to 0

Ex. x-2=0 x+6=0

a) Now solve...

x - 2 = 0 (Add 2 to both sides)

__+2

x=-2

x + 6 = 0 (Subtract 6 from both sides)

__- 6

x=6

b) Then you get your solution set {-2 , 6}

## How do we use Quadratic Equations and why?

We use Quadratic Equations in the real world by...