Solve the following quadratic equation using the perfect square trinomial pattern: 1/4 x^2 + 2x + 4 = 0

Answer 1

To solve the quadratic equation $\frac{1}{4}{x}^2+2x+4=0$ using the perfect square trinomial pattern, we first want to express it in a form that allows us to factor it as a perfect square.

1. Start by eliminating the fraction. We can multiply the entire equation by 4 to make calculations easier:

$$4(\frac{1}{4}{x}^2+2x+4)=4\cdot 0$$ $$x^2+8x+16=0$$

2. Now the equation is $x^2+8x+16=0$. Notice that $x^2+8x+16$ is a perfect square trinomial. It can be factored as:

$$(x+4{)}^2=0$$

3. Now, solve for $x$ by taking the square root of both sides:

$$x+4=0$$

4. Subtract 4 from both sides:

$$x=-4$$

Thus, the solution to the equation $\frac{1}{4}{x}^2+2x+4=0$ is:

$$\boxed{{\displaystyle -4}}$$