Solve the following quadratic equation using the perfect square trinomial pattern: 1/4 x^2 + x + 4
x = __
To solve the quadratic equation using the perfect square trinomial pattern, we need the equation in the form (x + a)^2 = b, where "a" and "b" are constants.
We can rewrite the given equation as (1/4)(x^2 + 4x +16):
1/4(x^2 + 4x + 16)
Now, we want to complete the square by adding and subtracting the same value in the parentheses to make it a perfect square trinomial.
1/4(x^2 + 4x + 4 + 12)
Next, we simplify the equation:
1/4[(x + 2)^2 + 12]
Now, we have the equation in the desired form, (x + a)^2 = b. In this case, a = 2 and b = 12.
Therefore, x = -a ± √(b) = -2 ± √(12) = -2 ± 2√(3).
Hence, the solution to the quadratic equation 1/4 x^2 + x + 4 is x = -2 ± 2√(3).