1/4 x^2 + x + 1 = 0 solve by factoring?

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

x^2 + 4x + 4 = 0

[x + 2]^2 = 0

x + 2 = sqrt {0} = 0

x = - 2

if you don't like the fraction in the beginning, you could always multiply the WHOLE equation by 4. That would give you:

x^2 + 4x + 4 = 0

That makes it a little easier to factor.

good luck

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

(x+2)^2 = 0

x = -2

There is only one real root since the discriminant is zero.

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

x + 2 = 0
x = -2

∴ x = -2