Solve the following quadratic equation using the perfect square trinomial pattern: 1/4 * x ^ 2 + 2x + 4 (1 point)
To solve the quadratic equation using the perfect square trinomial pattern, we need to find the square root of the first and last term, and then rewrite the middle term using the formula for the perfect square trinomial pattern.
The perfect square trinomial pattern is: (a + b)^2 = a^2 + 2ab + b^2.
In this case, the quadratic equation is 1/4x^2 + 2x + 4.
Taking the square root of the first term (1/4x^2) gives us (1/2x), and taking the square root of the last term (4) gives us (2).
Now, we can rewrite the middle term (2x) using the formula for the perfect square trinomial pattern.
The formula is a^2 + 2ab + b^2, where a = (1/2x) and b = (2).
So, we have (1/2x)^2 + 2(1/2x)(2) + (2)^2.
Simplifying this expression gives us (1/4x^2) + (2x) + 4.
Now we can see that the quadratic equation 1/4x^2 + 2x + 4 can be written as the perfect square trinomial pattern (1/2x + 2)^2.
Therefore, the solution to the quadratic equation using the perfect square trinomial pattern is (1/2x + 2)^2.
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The quadratic equation given is 1/4 * x^2 + 2x + 4.
To solve this quadratic equation using the perfect square trinomial pattern, we can rewrite it as (1/4)(x^2 + 8x + 16).
We can see that the trinomial x^2 + 8x + 16 can be factored into (x + 4)(x + 4), which is a perfect square trinomial.
Therefore, the quadratic equation can be written as (1/4)(x + 4)(x + 4).
To find the solutions, we can set each factor equal to zero and solve for x:
x + 4 = 0
x = -4
Therefore, the solution to the quadratic equation using the perfect square trinomial pattern is x = -4.