Derive the Quadratic Formula

2 0ax bx c c c

2ax bx c 2 b

a x x ca

2 ba x x c

a

212ba

2

24ba

2

24ba

2

24ba

a

2 2

2 4b b

a x ca a

2

4ba

2 2

2 4b b

a x ca a

a a2 2

22 4b b c

xa aa

The LCD is 4a2

2 2

2 2

42 4 4b b ac

xa a a

2

2

44

b aca

Same Denominator

2 2

2

42 4b b ac

xa a

2

2

42 4b b ac

xa a

2 42 2b b ac

xa a

2ba

2ba

2 42 2b b ac

xa a

2 42

b b acx

a

2 0ax bx c

2 42

b b acx

a

26 7 2 0x x a b c

2 4

2x

76 276

7 49 4812

x

7 1

12x

7 112

x

7 112

x

7 112

x

6

12

1

2

7 112

x

8

12

2

3