Question

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

Answer 1

To solve the quadratic equation \(x^{2} + x + 0.25 = 0\) using the perfect square trinomial pattern, we can rewrite the left side of the equation.

First, notice that \(0.25\) can be expressed as \((0.5)^2\). Therefore, we can rewrite the equation as:

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

This is a perfect square trinomial, and it can be factored as:

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

Now, we can solve for \(x\) by taking the square root of both sides:

\[
x + 0.5 = 0
\]

Subtracting \(0.5\) from both sides gives us:

\[
x = -0.5
\]

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

\[
\boxed{-0.5}
\]