Solve the following quadratic equation using the perfect square trinomial pattern: x2+x+0.25=0 .(1 point) Responses x=0.5 x equals 0.5 x=−0.5 x equals negative 0.5 x=0.25 x equals 0.25 x=−0.25 x equals negative 0.25
To solve the quadratic equation x^2 + x + 0.25 = 0, we can use the perfect square trinomial pattern.
The perfect square trinomial pattern states that (a + b)^2 = a^2 + 2ab + b^2.
Here, we have x^2 + x + 0.25. Notice that this can be written as (x + 0.5)^2, which matches the perfect square trinomial pattern. Thus, we can rewrite the equation as:
(x + 0.5)^2 = 0
Now, taking the square root of both sides, we get:
x + 0.5 = 0
Solving for x, we subtract 0.5 from both sides:
x = -0.5
Therefore, the correct answer is: x equals -0.5.