Question

Solve the following quadratic equation using the perfect square trinomial pattern: x2+x+0.25=0
(1 point)
Responses

x = 0.5
x = 0.5

x = -0.5
x = -0.5

x = -0.25

Answer 1

To solve the quadratic equation \(x^2 + x + 0.25 = 0\) using the perfect square trinomial pattern, we first rewrite the equation in a form that makes it easier to see the pattern.

The equation can be rewritten as:

\[
x^2 + x + \left(\frac{1}{2}\right)^2 = 0
\]

Here, \( \left(\frac{1}{2}\right)^2 = 0.25\). Now, we can express the left side as a perfect square:

\[
\left(x + \frac{1}{2}\right)^2 = 0
\]

To solve for \(x\), we take the square root of both sides:

\[
x + \frac{1}{2} = 0
\]

Now, isolate \(x\):

\[
x = -\frac{1}{2}
\]

So, the solution is:

\[
x = -0.5
\]

Thus, the correct response is:

**x = -0.5**