Equations-Transformable-into-Quadratic-Equations

1. Equations
Transformable into
Quadratic Equations
PREPARED BY:
MRS. LIEZEL A. SERRANO
SST - II

2. Can you tell if these are quadratic
equations or not?
x ( x – 5 ) - 36
(x+5)2 + (x-2)2 = 37
𝟔
𝒙
+
𝒙−𝟑
𝟒
= 𝟐
x +
𝟖
𝒙−𝟐
= 𝟏 +
𝟒𝒙
𝒙 −𝟐

3. Equations Transformable into Quadratic
Equations
◦There are equations that are transformable
into quadratic equation form. These
equations may be given in different forms.
Hence, the procedures in transforming
these equations into quadratic equations
may be also different.

4. Two Categories
◦Quadratic Equations that are NOT
WRITTEN IN STANDARD FORM
◦RATIONAL ALGEBRAIC EQUATIONS
that are transformable into
quadratic equations

5. Quadratic Equations
that are not written in
Standard Form

6. Example 1: x (x-5) = 36
x (x-5) = 36
x2 – 5x – 36 = 0

7. Example 2: 3x (x-8) = 2
3x (x-8) = 2
3x2 – 24x – 2 = 0

8. Example 3: (s – 6)2 = 15
(s – 6)2 = 15
s2 – 12s + 36 – 15 = 0
s2 – 12s + 21 = 0

9. Example 4: (a – 2)2 + (a – 3)2 = 9
(a – 2)2 + (a – 3)2 = 9
(a2 – 4a + 4) + (a2 – 6a + 9) – 9 = 0
2a2 – 10a + 13 – 9 = 0
2a2 – 10a + 4 = 0

10. Example 5: (2r + 3)2 + (r + 4)2 = 10
(2r + 3)2 + (r + 4)2 = 10
(4r2 +12r + 9) + (r2 + 8r + 16) – 10 = 0
5r2 + 20r + 25 – 10 = 0
5r2 + 20r + 15 = 0

11. RATIONAL ALGEBRAIC
EQUATIONS that are
transformable into
quadratic equations

12. Example 6:
1
𝑥
+
2𝑥
5
= 0
1
𝑥
+
2𝑥
5
= 0
(
1
𝑥
+
2𝑥
5
= 0) (x)(5)
1(𝑥)(5)
𝑥
+
2𝑥(𝑥)(5)
5
= 0
5 + 2x2 = 0
2x2 + 5 = 0

13. Example 7:
6
𝑥
+
𝑥−3
4
= 2
24 + (x2 – 3x) = 8x
24 + x2 – 3x – 8x = 0
x2 – 11x + 24 = 0
6
𝑥
+
𝑥−3
4
= 2
(
6
𝑥
+
𝑥−3
4
= 2) (x)(4)
6 (𝑥)(4)
𝑥
+
(𝑥−3)(𝑥)(4)
4
= 2(x)(4)

14. Example 8: x +
𝟖
𝒙−𝟐
= 𝟏 +
𝟒𝒙
𝒙 −𝟐
x +
𝟖
𝒙−𝟐
= 𝟏 +
𝟒𝒙
𝒙 −𝟐
(x +
𝟖
𝒙−𝟐
= 𝟏 +
𝟒𝒙
𝒙 −𝟐
) (x-2)
x (x−2) +
𝟖(𝒙−𝟐)
𝒙−𝟐
= 𝟏(𝒙 − 𝟐) +
𝟒𝒙(𝒙−𝟐)
𝒙 −𝟐
)
x2 – 2x + 8 = x – 2 + 4x
x2 – 2x + 8 - x + 2 - 4x = 0
x2 – 7x + 10 = 0

15. Example 9:
𝟔
𝒔−𝟓
+
𝒔 −𝟓
𝟐
= 𝟑
𝟔
𝒔−𝟓
+
𝒔 −𝟓
𝟐
= 𝟑
(
𝟔
𝒔−𝟓
+
𝒔 −𝟓
𝟐
= 𝟑) (s-5)(2)
𝟔 (𝒔−𝟓)(𝟐)
𝒔−𝟓
+
(𝒔 −𝟓)(𝒔−𝟓)(𝟐)
𝟐
= 𝟑(s-5)(2)
12 + (s2 – 10s + 25) = 6(s-5)
12 + s2 – 10s + 25 = 6s – 30
12 + s2 – 10s + 25 – 6s + 30 = 0
s2 – 16s + 67 = 0

16. Change the following to quadratic
equations in standard form.
1.(m – 4)2 + (m – 7)2 = 15
2.
𝟐𝒙𝟐
𝟓
+
𝟓𝒙
𝟒
= 𝟏𝟎
3.
𝟐
𝒃
−
𝟑𝒃
𝟐
= 𝟕
4.
𝟑
𝒙
−
𝟒
𝟐𝒙
= −𝟏
5.
𝟐
𝒓−𝟏
−
𝟒
𝒓+𝟓
= 𝟏