Solve the following quadratic equation using the perfect square trinomial pattern: x2+x+0.25=0 .(1 point) Responses x=−0.5 x equals negative 0.5 x=−0.25 x equals negative 0.25 x=0.5 x equals 0.5 x=0.25
The given quadratic equation is x^2 + x + 0.25 = 0.
To solve this equation using the perfect square trinomial pattern, we can rewrite the equation as follows:
(x + 0.5)^2 = 0.
Setting (x + 0.5)^2 = 0, we can take the square root of both sides to find that x + 0.5 = 0.
Solving for x, we subtract 0.5 from both sides:
x = -0.5.
Therefore, the solution to the quadratic equation using the perfect square trinomial pattern is x = -0.5.
So, the correct response is x equals -0.5.
To solve the quadratic equation x^2 + x + 0.25 = 0, we can first rewrite it in the form of a perfect square trinomial.
The pattern for a perfect square trinomial is (a + b)^2 = a^2 + 2ab + b^2.
In this case, we want to find values of a and b that make the left side equal to the right side of the equation. Let's look at the equation x^2 + x + 0.25 = 0.
We can see that the term 0.25 is already in the form of a perfect square (0.5^2 = 0.25).
So, we can rewrite the equation as (x + 0.5)^2 = 0.
Now, we can take the square root of both sides to solve for x:
√((x + 0.5)^2) = √0
Therefore, x + 0.5 = 0
To isolate x, we can subtract 0.5 from both sides of the equation:
x = -0.5
Therefore, the solution to the quadratic equation x^2 + x + 0.25 = 0 is x = -0.5.
To solve the quadratic equation x^2 + x + 0.25 = 0 using the perfect square trinomial pattern, follow these steps:
Step 1: Identify the coefficients of the equation:
In this case, the quadratic equation is written in the form ax^2 + bx + c = 0. From the given equation, we have:
a = 1
b = 1
c = 0.25
Step 2: Rewrite the equation in the form of a perfect square trinomial:
A perfect square trinomial is of the form (x + k)^2 = x^2 + 2kx + k^2. In this case, we need to find the value of k that makes the equation a perfect square trinomial.
Looking at the given equation, x^2 + x + 0.25, we can see that the coefficient of x is 1. In order to have a perfect square trinomial, we need to have 2kx, which means 2k = 1. Therefore, k = 1/2.
We can rewrite the equation x^2 + x + 0.25 as:
(x + 1/2)^2 = x^2 + 2(1/2)x + (1/2)^2
(x + 1/2)^2 = x^2 + x + 1/4
Step 3: Set the equation equal to zero:
(x + 1/2)^2 = 0
Step 4: Solve for x:
Taking the square root of both sides of the equation, we get:
x + 1/2 = 0
Solving for x, we have:
x = -1/2
Finally, the solution to the quadratic equation x^2 + x + 0.25 = 0 using the perfect square trinomial pattern is:
x = -0.5