Solve the following quadratic equation using the perfect square trinomial pattern: x^2+x+0.25=0

Question

.(1 point)
Responses

x=−0.25
x equals negative 0.25

x=0.25
x equals 0.25

x=−0.5
x equals negative 0.5

x=0.5

Answer 1

To solve the quadratic equation \(x^2 + x + 0.25 = 0\) using the perfect square trinomial pattern, we can rewrite it in the form \((x + a)^2 = b\).

First, we notice that the equation can be rearranged as follows:

1. Recognize that \(0.25\) is \((0.5)^2\).
2. The given expression can be rewritten as:

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

3. Now we can identify since our equation matches the pattern of a perfect square trinomial, we can rewrite it:

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

4. Now, take the square root of both sides:

\[ x + 0.5 = 0 \]

5. Solving for \(x\):

\[ x = -0.5 \]

Thus, the solution to the equation \(x^2 + x + 0.25 = 0\) is:

\[ x = -0.5 \]

So the correct response from the options provided is:

x = -0.5 (x equals negative 0.5)