Question

solve $2x^2 + x - 4 = 0$.
$x^2 + \boxed{1/2} \boldsymbol{\checkmark} x + \boxed{-2} \boldsymbol{\checkmark} = 0$
\textbf{complete}
$x^2 + \frac{1}{2}x + \boxed{1/16} \boldsymbol{\checkmark} = 2 + \boxed{1/16} \boldsymbol{\checkmark}$
\textbf{complete}
$(x + \boxed{1/4} \boldsymbol{\checkmark})^2 = \boxed{33/16} \boldsymbol{\checkmark}$
\textbf{complete}
choose the solution to the equation.
\bigcirc $-\frac{1}{4} \pm \frac{\sqrt{33}}{4}$
\bigcirc $-\frac{1}{2} \pm \frac{\sqrt{33}}{4}$
\bigcirc $\frac{1}{4} \pm \frac{\sqrt{33}}{4}$
\textbf{done} \boldsymbol{\checkmark}

Explanation:

Step1: Isolate square root term

Take square root of both sides:
$$x+\frac{1}{4} = \pm\sqrt{\frac{33}{16}}$$

Step2: Simplify the square root

Simplify the radical expression:
$$\sqrt{\frac{33}{16}} = \frac{\sqrt{33}}{4}$$

Step3: Solve for x

Subtract $\frac{1}{4}$ from both sides:
$$x = -\frac{1}{4} \pm \frac{\sqrt{33}}{4}$$

Answer:

$-\frac{1}{4} \pm \frac{\sqrt{33}}{4}$