Solve the following quadratic equation using the perfect square trinomial pattern: x^2+x+0.25=0 .(1 point) Responses x=0.25 x equals 0.25 x=−0.5 x equals negative 0.5 x=−0.25 x equals negative 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:

1. Notice that \( x^2 + x + 0.25 \) can be factored as a perfect square: \[ x^2 + x + 0.25 = \left( x + 0.5 \right)^2 \]

2. Therefore, we can rewrite the equation: \[ \left( x + 0.5 \right)^2 = 0 \]

3. Now, take the square root of both sides: \[ x + 0.5 = 0 \]

4. Solving for \( x \): \[ x = -0.5 \]

Thus, the solution to the equation \( x^2 + x + 0.25 = 0 \) is: \[ x = -0.5 \]

The correct response from the options is \( x = -0.5 \) (x equals negative 0.5).