Question

Solve the following equation by completing the square. 1/4x^2+x+1/4=0

A. X=-2+sqrt(3) or x=2-sqrt(3)
B. X=1 or x=-5
C. X=2+sqrt(3) or x=2-sqrt(3)
D. X=-2+sqrt(3) or -2-sqrt(3)
Please and Thank you!

Answer 1

Answer: D. X= -2+sqrt(3) or -2-sqrt(3)

Explanation:

The person at the top is right, i got 100 on my test

Answer 2

D. X=-2+sqrt(3) or -2-sqrt(3)

`x_(1) =-2+√(3) \\x_(2) =-2-√(3)`

Explanation:

Quadratic Equation given:

`$(1)/(4) x^2+x+(1)/(4)=0$`

In order to get rid of the fractions, multiply both sides by 4.

`$(1)/(4)x^2\cdot \:4+x\cdot \:4+(1)/(4)\cdot \:4=0\cdot \:4$`

We get:

`x^2+4x+1=0`

`x^2+4x+4-4+1=0`

Completing the square:

`(x+2)^2-4+1=0\\`

`(x+2)^2-3=0`

`(x+2)^2=3`

`x+2=\pm√(3)`

`x=-2\pm√(3)`

`x_(1) =-2+√(3) \\x_(2) =-2-√(3)`