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

Question

Solve the following equation:

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

00:00 Find X

00:04 Identify the coefficients

00:16 Use the roots formula

00:38 Substitute appropriate values according to the given data and solve

00:57 Calculate the squares and products

01:07 A root of 0 is always equal to 0

01:19 When the root equals 0, there will be only one solution to the equation

01:42 And this is the solution to the question

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 $x = -\frac{1}{2}$ .

$x=-\frac{1}{2}$