The document discusses various equations that can be transformed into quadratic equations, categorizing them into those not in standard form and rational algebraic equations. It provides multiple examples illustrating how to convert these equations into standard quadratic form. The document serves as an educational resource prepared by Mrs. Liezel A. Serrano for understanding the transformation of equations 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 +

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: + = 0
+ = 0
+ = 0) (x)(5)
+ = 0
5 + 2x2
= 0
2x2
+ 5 = 0

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

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

15. Example 9:
((s-5)(2)
(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.
3.
4.
5.