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

Question

.(1 point)

Answer 1

To solve the quadratic equation using the perfect square trinomial pattern, we need to rewrite the equation in the form (x + a)^2 = 0.

In this case, we have x^2 + x + 0.25 = 0.

We can rewrite 0.25 as (0.5)^2 and rewrite the equation as:

x^2 + x + (0.5)^2 = 0.

Now we can recognize that (x + 0.5)^2 = 0.

Therefore, x + 0.5 = 0.

Solving for x, we subtract 0.5 from both sides:

x = -0.5.

So the solution to the equation x^2 + x + 0.25 = 0 is x = -0.5.