How to Solve Quadratic Equations
Banana Mango and Mely
Ways we use Quadratic Equations Everyday
Problem:
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