Solve the following equation using the perfect square trinomial pattern: x^2+x+0.25=0 (1 point) Responses x = 0.25 x = 0.25 x = - 0.5 x = - 0.5 x = - 0.25 x = - 0.25 x = 0.5

Answer 1

To solve the equation x^2+x+0.25=0 using the perfect square trinomial pattern, we need to rewrite the equation as a perfect square.

The perfect square trinomial pattern is (a+b)^2 = a^2+2ab+b^2.

In this case, (a+b)^2 = x^2 + 2(0.5)(x) + (0.5)^2 = x^2 + x + 0.25.

So, we can rewrite the equation x^2+x+0.25=0 as (x+0.5)^2=0.

Only when a perfect square equals zero, the square root of that whole expression can equal zero.

Therefore, the solutions to the equation are x = -0.5.

So, the correct response is x = - 0.5.