Solving for X in the Equation: x^2 + x + 1/4 = 0

Solve the following equation:

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

To solve the quadratic equation $x^2 + x + \frac{1}{4} = 0$, we will use the method of completing the square:

• Step 1: Rewrite the equation focusing on forming a perfect square.
• Step 2: The expression $x^2 + x$ can be transformed into a perfect square.
• Step 3: Note that $(x + \frac{1}{2})^2 = x^2 + x + \frac{1}{4}$.
• Step 4: Substitute into the equation: $(x + \frac{1}{2})^2 = 0$.
• Step 5: Solve for $x$: If $(x + \frac{1}{2})^2 = 0$, then $x + \frac{1}{2} = 0$.
• Step 6: Simplifying the equation, we find $x = -\frac{1}{2}$.

This means the solution to the quadratic equation is $x = -\frac{1}{2}$.

Thus, the correct answer is $x = -\frac{1}{2}$.