transformable equation

1. MATHEMATICS 9
Solving Equations Tronsformoble toquadratic
Equation Including Rational Algebraic
Equations
Lesson1: Solving quadratic Equations ThatAreNot
WrittenInStandardForm
Lesson 2: Solving Rational Algebraic Equations
, Transformable Toquadratic Equations
•

2. Lesson 1:Solving Quadratic Equations That
Are Not Written InStandard Form
In solving quadratic equation that is not written in standard form,
transform the equation in the standard form W + éz + r = 0 where a,
h, and c are real numbers and o / 0 and then, solve the equation
using any method in solving quadratic equation(extracting square
roots, factoring, completing the square, or quadmtic formula).

3. Solution:
Ttansform the équation in standard form.
x(.r —
5) = 36
- Si - 36
./ —
5x —
36 = 0
Solve the equation using any method.
By factoring
—
5 —
36 = 0
(x—
9)(.v+ 4)= 0
—9=0 i+4=0
x-9 -——4
• The solution set of the equation is ]9, —
4}.

4. E¥aasple 2: Sotie + 5)’ +{a--2)’ = 37.
Transfonn thecqu8tion inetoodard dorm.
. ' + l0r+ 25*6 -4z+ 4=37
W + 6r * 29- 3? —
• W + 6r* 29- 37- 0
. ’ * r - 4 =0 Divide all terinsby2.
Solvethecquationusinganymethod.
By £actoring
* 3z- 4- 0
(x+ 4}{‹— ț)= 0
x + 4 - 0
x=—4
• The solution set of the equatinn is ț
—4, lJ.

5. Transform tficequaiion iiistandard font.
2.x“ —
3i-= r“ * l4
b- - .N —
5. —
14 = 0
Suite lhc cquuticn usinj; uny method.
By C‹iuadmtic Fnnnula. identify the values nFr‹. ñ. and c'
2n tt1) 2 2 " 2
Thc solution set of the equstion is (
— 2, 7).

6. Transform the equation in standard form.
y —4)*= 4
—
8r * 16 = 4
—
&
x* 16 —4= 0
—
&r* l2 = 0
Solve theequation using any method.
By factoring
—
8x+ 12= 0
(x —
6)(x—
2)= 0
x-6=O
•Thesolution set of theequation is {6, 2}.
x —
2= 0
x = 2

7. Trawrorro the aquatic+rt in siandazd Fc+rizu
%+*O -*$=O
F• 13. • 1-0
B§' JralJu Fumutly idci tiI'y the YaTacs oFu. it, snJ '
• The solution set of the equation is (
—2, —
).

8. Lesson2: Solving RationalAlgebraicEquations
Transformable To Quadratic Equations
There are rational equations that can be transformed
into quadratic equation of the fonn ox2 + 6x + r = 0 where a,
b and r are real numbers, and o / 0 and it can be solved
using the different methods in solving quadratic equation.

9. Multiply bpth sides of the equaliun by the Levsl Cummun
Multiple (LCM) or Leaxt Commun Denominator (LCD).
dratic equation in standard form.
Solve theequation using any method in solving quadratic
Check whether the obtained 'aIucs ot”.i’ soisfics the given

10. Example I: Solve the rational algebraic erjualion -I- “ = 2.
1. Multiply bolli sideof ltte equation by the LCD, the LCD is 4s.
Transform the resulting equation in suindard Fume.
3. Solve the equation using any method. Since the equation is fâclorablc,
. + 24 = 0 ‹ —3 = 0 .z—8= 0
The solution set of the equation is (3, 8).

12. Example 3: Solvetltcrational algebraic e
q
u
a
tion z + = l + ’ .
I. Multiply both s
i
d
eof t
h
eequalion bytteLCD, t
h
eU
D isx- 2.
x—
2( + - x—
2(›+ ) —
• .ix- 2)+ 8= I(.x- 2)+
.4z
2. Transform theresulting equation in slandcrd for.
.x' - 2z+ 8 Sz- 2 .ñ- 1z- S
z+ 8+ 2= 0
' - 7
x+ I0- 0
3. Solvet
h
eequation usinga
n
ymethod. Sincet
h
eequation islacombl¢.
z'- 7z+ 1
0- 0
t
x- 'j)t. - 2)- 0
x- 5- 0
.c 5
.r- 2- 0
x= 2
• The solution set of the equation is{5, 2}.

13. Example 4: Solvé ilie rniionol algcbniic equation + = 4.
The solution set of ‹he equation is (s + W6,6 — .