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)