Question

--4 x square + 4 root 3 X + 3 equal to zero by completing the square method ​

Answer 1

Answer:

4x² + 4√3x + 3 = 0

Divide all terms by 4(coefficient of x²)

x² + √3x +3/4 = 0x² + √3x = -3/4

Multiply and divide by 2.

x² + 2(x)(√3/2) = -3/4

Add (√3/2)² on both sides.

x² + 2(x)(√3/2) + (√3/2)² = -3/4 + 3/4 = 0

L.H.S is in the form of a² + 2ab + b² = (a + b)²

So,

(x + √3/2)² = 0x + √3/2 = ±√0 = ±0 = 0

x = -√3/2

Answer 2

Answer:

x= -√3/2 , -√3/2

Step-by-step explanation:

4x²+4√3x+3=0

divide the equation by 4,we get

x²+√3x+3/4=0

adding [(1/2)(coefficient of x)²] on both sides

x²+√3x+[(1/2)√3]²+3/4=[(1/2)√3]²

x²+√3x+[√3²/4]+3/4=[√3²/4]

x²+√3x+3/4+3/4=3/4

x²+√3x+3/4=3/4-3/4

x²+√3x+3/4=0

(x+√3/2)²=0

(x+√3/2)(x+√3/2)=0

x+√3/2=0                     x+√3/2=0

x= -√3/2                       x= -√3/2