Question

Q1.solve 2x^2 _ 10x _ 3 =0 by completing the square method

Answer 1

Explanation:

2x²-10x-3=0

Step 1: Divide the whole Equation with the coefficient of x².

=> x²-5x-3/2=0 [ 0÷2=0]

=> x²-5x-3/2=0

We know that : (a-b)²= a²+b²-2ab

Here , a= x

so, -2ab= -5x

-2xb= -5x

b= -5x/-2x = 5/2

b= 5/2

Come to the Equation

=> x²-5x-3/2=0

Adding and subtracting ( 5/2 )²

=> x²-5x-3/2+(5/2)²-(5/2)²

=>x²+(5/2)² -5x-3/2 -(5/2)²

=> (x-5/2)²-3/2-(5/2)²

=>(x-5/2)²-3/2 -25/4

=> (x-5/2)²-6-25/4

=> (x-5/2)² -31/4=0

=> (x-5/2)²= 31/4

=> x - 5/2 = ±31/4

x= 31/4+5/2

x= 31+10/4

x= 41/4

x= -31/4+5/2

x= -31+10/4

x= -21/4