Question

can anyone teach me the completing the square method in quadratic equations?

Answer 1

Step 1:
Divide the equation by the coefficient of x2.
Step 2:
Divide the coefficient of x by 2 and add and subtract its square,
Step 3:
Take the subtracted square and the constant term to the next side and solve it.
Step 4:
In the RHS it will be as a equation. (a+b)2 or (a-b)2.
Step 5:
Take square root on both the side. From RHS take the constant term alone to the other side and solve it.
Step6:
You got the answer.

Example :
Step 1
2x^2 + 10 x +3= 0
x^2 + 5x +3/2 =0
Step 2
x^2 + 5x +(5/2)^2- (5/2)^2 + 3/2= 0
Step 3 and 4
x^2 + 5x+(5/2)^2= (5/2)^2 - 3/2
(x+5/2)^2 = 25- 6/4
(x+5/2 )^2 = 19/4
Step 5
x+5/2 =√19/√4
x+5/2 = √19/2
x = -5/2 +√19/2 or -5/2 - √19/2
Step 6
x= -5+√19/2 or -5 -√19/2

Hope it helps