Solve the following quadratic equation using the perfect square trinomial pattern: x2+x+0.25=0

Question

.(1 point)
Responses

x=0.25
x equals 0.25

x=0.5
x equals 0.5

x=−0.5
x equals negative 0.5

x=−0.25

Answer 1

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

Notice that \( 0.25 \) is \( \left( \frac{1}{2} \right)^2 \). We can rewrite the equation:

\[ x^2 + x + \left( \frac{1}{2} \right)^2 = 0 \]

Now, we can express the left side as a perfect square:

\[ \left( x + \frac{1}{2} \right)^2 = 0 \]

To solve for \( x \), we take the square root of both sides:

\[ x + \frac{1}{2} = 0 \]

Now, solving for \( x \):

\[ x = -\frac{1}{2} \]

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

\[ x = -0.5 \]

So, the correct response is:

x = -0.5 (or "x equals negative 0.5").