# How to Solve Quadratic Equations

### Banana Mango and Mely

## Ways we use Quadratic Equations Everyday

## Problem:

**5r² - 44r + 20 = -30 + 11r**

## Step 1

Move all the numbers to one side of the equation, so it ends up being equal to 0 -

5r² - 44r + 120 + 30 = -30 + (30) + 11r

*Add +30 to the 120 so it becomes 150, and it cancels the -30 out on the other side of the equation*

5r² - 44r +150 = 11r

*Subtract 11r on both sides*

5r² - 44r - 11r +150 = 0

*Combine like terms*

**5r² - 55r + 150 = 0**

## Step 2

Multiply *A (5)* and *C (150) *then find the factors of that product that add up to -55;

5 × 150 = 750

*Find factors of 750 that add up to -55*

-30 × -25 = 750

-30 - 25 = -55

**5r² - 30r - 25r + 150 = 0**

## Step 3

Factor the equation;

5r² - 30r - 25r + 150 = 0

=

**5r (r - 6) - 25 (r - 6)**

## Step 4

*Set each part of the equation equal to zero;*

r - 6 = 0

5r - 25 = 0

*Use inverse operations to solve each separate equation*

r - 6 = 0 + (6)

**r = 6**

5r - 25 = 0 + (25)

__5r = 25__

5

**r = 5**

## Answer:

**{ 5 , 6 }**

## Check #1

5 (5)² - 30 (5) - 25 (5) + 150

5 (25) - 150 - 125 + 150

*The 150's cancel each other out*

5 (25) - 125

125 - 125

=

0

## Check #2

5 (6)² - 30 (6) - 25 (6) +150

5 (36) - 180 - 150 + 150

*The 150's cancel each other out*

*5 (36) - 180*

*180 - 180*

*=*

*0*