# Solving Quadratic Equations

### -Angelina Melendez Negron & Abigail Mercado

## We will show you the steps on how to solve 2 quadratic equations

## What are the steps for (x^2-2x+1=0)

## SIMPLE EQUATION

## Step 1:

**Find the factors of 1 that when you add equals to -2**

**Factors of 1:**

**-1,-1 = -2**

## Step 2:

**Plug in x in 2 set of parentheses**

**(x **** **** ) (**** **** )**

## Step 3:

**Plug in the 2 factors from step 1 that equalled to -2 into the parenthesis (-1,-1)**

(x-1) (x-1)

## Step 4:

**make each set of parenthesis equal 0**

x-1=0

x-1=0

## Step 5:

**try to get everything on one side**

x-1=0 (ADD 1 ON BOTH SIDES)

-1+1=cancels out to 0

1+0= 1

x=1

x-1=0 (ADD 1 ON BOTH SIDES)

-1+1=cancels out to 0

1+0=1

x=1

## Step 5:

**plug into brackets**

{1,1} <answer

## What are the steps for (7x^2+21x-28=0)

## Step 1:

**You have to multiply 7 and -28 to get x^2 alone**

7x-28=-196

## Step 2:

**Now we have to find the factors of -196 that when you add equal to 21**

**Factors-**

28,-7=21

## Step 3:

**Rewrite the equation (plug in factors)**

7x^2+28x-7x-28=0

## Step 4:

**Find the factors of the first set and plug in**

|7x^2+28x|-7x-28=0

- take out a x from 7x^2 which would be 7x
- put 7x outside of the parenthesis
- put the remainder x inside the parenthesis 7x(x)
- divide 28 by 7 which gives you 4
- put the 4 inside the parenthesis which would be 7x(x+4)

## Step 5:

**Find the factors of the second set and plug in**

7x^2+28x|-7x-28|=0

- take out a x from -7x which would be -7
- put -7 outside the new set of parentheses
- put the remainder x inside the parenthesis -7(x)
- divide -28 by -7 which gives you 4
- put the 4 inside the parenthesis which would be -7(x+4)

## Step 6:

**Combine the 2 sets that we did in step 4 and step 5**

7x(x+4)-7(x+4)

## Step 7:

**Put the 2 outside numbers from both sets and combine them into 1 set**

**7x**(x+4)**-7**(x+4)

(7x-7)

## Step 8:

Since the 2 closed parenthesis have the numbers in them we make it as one

7x**(x+4)**-7**(x+4)**

**(x+4)**

## Step 9:

**Put the 2 parenthesis that we created in step 7 and step 8 side by side**

(7x-7)(x+4)

## Step 10:

**Put both parenthesis to equal 0**

7x-7=0

x+4=0

## Step 11:

**Solve the equations that we made in step 10**

7x-7=0** **

**!get everything to 1 side!**

**add 7 on both sides **

0+7=7

-7+7=0

7x=7

**divide by 7 on both sides **

7x/7= x

7/7=1

**so now we know that one of our solutions is x=1**

x+4=0

**!get everything to 1 side!**

**subtract 4 on both sides **

0-4=-4

4-4=0

**so now we know that the second solution is x=-4**

## FINAL STEP:

**Plug both of our solutions that we got in step 11 into brackets**

{1,4} <answer