QUADRATIC FORMULA
x=
−b ±
√
b2 − 4ac
2a
Original equation: 2x2 − 3x − 15 = 5
Step 1:
Set the equation equal to zero.
Subtract −5 from both sides
2x2 − 3x − 15 − 5 = 5 − 5
2x2 − 3x − 20 = 0
Step 2:
Identify a, b, c.
Use the standard form of a quadratic equation: ax2 + bx + c = 0
a = 2,
Step 3:
b = −3,
c = −20
Use the Quadratic Formula √
3a: Substitute and solve for b2 − 4ac
√
= pb2 − 4ac
= p(−3)2 − 4(2)(−20)
= √ 9 − (−160)
= 169
= 13
So the
√
b2 − 4ac = 13
3b: Calculate 2a
= 2a = 2(2) = 4
So 2a = 4
3c: Substitute steps 3a & 3b into the quadratic formula.
3c: Next, substitute for −b then simplify the fraction.
x=
x=
−b ±
√
b2 − 4ac
−(−3) ± 13
3 ± 13
=
=
2a
4
4
3 + 13
=⇒ x = 4
4
x=
3 − 13
−5
=⇒ x =
4
2
!
Assignment
1. x2 + 2x − 3 = 0
2. 2x2 − 3x − 15 = 5
3. 5x2 = 80
4. 9x2 − 7x − 4 = 0
5. 10x2 + 4x − 16 = x2