1. 7-4 EQUATIONS
IN QUADRATIC
FORM
BY: ENGELS ZELAYA

2. STUDY THE THREE EQUATIONS BELOW AND
NOTE THEIR SIMILARITY
 𝑥2 − 5𝑥 − 6 = 0 This equation is quadratic in x
 3𝑥 − 2 2
− 5 3𝑥 − 2 − 6 = 0 This equation is quadratic in 3x-2
 (
1
2
)2
−5
1
2𝑥
− 6 = 0 This equation is quadratic in 1/2x

3. EXAMPLE 1
 3𝑥 − 2 2
− 5 3𝑥 − 2 − 6 = 0
 Change variable
 W=3x-2
 𝑤 2 − 5 𝑤 − 6 = 0
 𝑤2
− 5𝑤 − 6 = 0
 A=1 B=-5 C=-6
 𝑊 =
−𝑏± 𝑏2−4𝑎𝑐
2𝑎
 𝑊 =
−(−5)± (−5)2−4(1)(−6)
2(1)
𝑊 =
5 ± 25 + 24
2
𝑊 =
5 ± 49
2
𝑊 =
5 ± 7
2
𝑊 =
5 + 7
2
𝑊 =
12
2
𝑊 = 6
𝑊 =
5 − 7
2
𝑊 =
−2
2
𝑊 = −1
𝑊 = 6
3𝑥 − 2 = 6
3x=6+2
3x=8
𝑥 =
8
3
W=-1
3x-2=-1
3x=-1+2
3x=-1
𝑥 =
1
3