How to Solve Quadratic Equations

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Ways we use Quadratic Equations Everyday

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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