Question

solve $2x^2 + x - 4 = 0$.
$x^2 + \boxed{1/2} x + \boxed{-2} = 0$
complete
$x^2 + \frac{1}{2}x + \boxed{1/16} = 2 + \boxed{1/16}$
complete
$(x + \boxed{})^2 = \boxed{}$

Explanation:

Step1: Identify square's linear term

For $x^2+\frac{1}{2}x$, the coefficient of $x$ is $\frac{1}{2}$. Half of this value is $\frac{1}{2} \times \frac{1}{2} = \frac{1}{4}$. This fills the first blank.

Step2: Simplify right-hand side

Calculate $2 + \frac{1}{16}$:
$$2 + \frac{1}{16} = \frac{32}{16} + \frac{1}{16} = \frac{33}{16}$$
This fills the second blank.

Answer:

$\frac{1}{4}$, $\frac{33}{16}$