KOLEKSI SIRI PERTAMA QUANTUM COOL-ACTIVE: MATHEMATICS SIMPLIFIED : FROM BASICS TO BRILLIANCE

coefficient of x 2 will

be 1.

SummarySummary

KeypointsKeypoints NotesNotes

COMPLETING THE SQUARECOMPLETING THE SQUARE

Steps:

(i) Coefficient of 푥² is 1 

(ii) Add both sides with  (b/2)²

(iii) The left side is factorized

into complete square

(iv) Solve by taking the square

root both sides

EXAMPLE

(i) 푥²+ 6푥 − 3 = 0

Solution:

푥² + 6푥 = 3

(ii) 푥² + 6푥 + (6/2)² = 3 + (6/2)²

(iii) 푥² + 6푥 + 3² = 3 + 3²

(iv) (푥 + 3)² = 3 + 9

(푥 + 3)² = 12

푥 + 3 = ±√ 12

푥 + 3 = √ 12 or 푥 + 3 = -√ 12

푥 = −3 + √12 or 푥 = −3 − √ 12

푥 = 0.464 or 푥 = −6.464

Solution set: {푥: 푥 = 0.464 or 푥 = −6.464}

If a is not equal to 1

Step 1 : divide the

by a such that the

complete equation

Step 2 : Now add the

coefficient of term-x,

square of half of the

(b/ 2 a)², on both sides.

Step 3 : Take the

square root on both

the sides.

Step 4 : Solve for

variable x and find

the roots

It is a process where consider a quadratic equation of the

ax² + bx + c = 0 and change it to write it in perfecting the

square form a(x + p) 2 + q = 0. This method is useful to

convert a quadratic expression from standard form into

vertex form especially for graph quadratic functions.