Question

Solve the following quadratic equation using the perfect square trinomial pattern: x^2+x+0.25=0
.(1 point)
Responses

x=−0.5
x equals negative 0.5

x=0.5
x equals 0.5

x=0.25
x equals 0.25

x=−0.25
x equals negative 0.25

Answer 1

To solve the quadratic equation \(x^2 + x + 0.25 = 0\) using the perfect square trinomial pattern, we first observe that the left-hand side can be expressed as a perfect square.

The expression \(x^2 + x + 0.25\) can be rewritten as:

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

This matches the form of a perfect square trinomial \((a + b)^2 = a^2 + 2ab + b^2\) where \(a = x\) and \(b = \frac{1}{2}\). Therefore, we can factor it as:

\[
(x + 0.5)^2 = 0
\]

Next, we take the square root of both sides:

\[
x + 0.5 = 0
\]

Now, we solve for \(x\):

\[
x = -0.5
\]

Thus, the solution to the quadratic equation is:

\[
\boxed{-0.5}
\]

So, the correct response is \(x = -0.5\).