Question

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

Answer 1

Answer:

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

$x_{1} =-2+\sqrt{3} \\x_{2} =-2-\sqrt{3}$

Step-by-step explanation:

Quadratic Equation given:

$\frac{1}{4} x^2+x+\frac{1}{4}=0$

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

$\frac{1}{4}x^2\cdot \:4+x\cdot \:4+\frac{1}{4}\cdot \:4=0\cdot \:4$

We get:

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

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

Completing the square:

$(x+2)^2-4+1=0$

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

$(x+2)^2=3$

$x+2=\pm\sqrt{3}$

$x=-2\pm\sqrt{3}$

$x_{1} =-2+\sqrt{3} \\x_{2} =-2-\sqrt{3}$