The document contains solutions to two quadratic equations. The first equation is solved by factorizing into (x - 1)2 = 4, giving solutions of x = 3 and x = -1. The second equation is completed by completing the square, giving (x + 5/2)2 = 121/4 and solutions of x = 3 and x = -8.

2. 1. 4x2 = 8x + 12
Solution:
4x2 – 8x = 12
4x2
𝟒
-
8x
𝟒
=
𝟏𝟐
𝟒
x2 – 2x = 3
= -
−𝟐
𝟐
= (-1)2 = 1
x2 – 2x + 1 = 3 + 1
(x – 1)2 = 4
(x – 1)2 = 4
(x – 1)2 = 𝟒
(x – 1) = ± 2
x – 1 = 2 and x – 1 = -2
x = 2 + 1 and x = -2 + 1
x = 3 and x = -1

3. 2. 2x2 + 10x = 48
Solution:
2x2
2
+
10𝑥
2
=
48
2
x2 + 5x = 24
5
2
= (
5
2
)2 =
25
4
x2 + 5x +
25
4
= 24 +
25
4
x2 + 5x +
25
4
=
96+25
4
x2 + 5x +
25
4
=
121
4
(x +
5
2
)2 =
121
4
x +
5
2
= 121
4
x +
5
2
= ±
11
2
x =
11
2
-
5
2
and x = -
11
2
-
5
2
x =
6
2
and x =
−16
2
x = 3 and x = -8