Question

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

Answer 1

Step-by-step explanation:

2x^2-10x-3=0 here using formula -b±✓(b^2-4ac)/2a to find roots here by comparing the equation with ax^2+bx+c a=2,b=-10,c=-3 keeping the values in the equation -(-10)±✓((-10)^2-(4×2×(-3) /2×2 we get (10±√124)/4 by simplifying we get ( 5±√31)/2 hence we get two roots x= (5+√31)/2 or (5-√31)/2

Answer 2

$\sf\huge {\underline{\underline{{Solution}}}}$

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