Solve the Equation: x²/4 + x + 1 = 0 Step-by-Step

Solve the following equation:

$\frac{x^2}{4}+x+1=0$

To solve the equation $\frac{x^2}{4} + x + 1 = 0$, we first rewrite it in the standard quadratic form:

$\frac{x^2}{4} + x + 1 = 0$ becomes $\frac{1}{4}x^2 + x + 1 = 0$.

Identifying the coefficients, we have:

• $a = \frac{1}{4}$
• $b = 1$
• $c = 1$

Next, we use the quadratic formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$. Plugging in the coefficients, we get:

$x = \frac{-1 \pm \sqrt{1^2 - 4 \cdot \frac{1}{4} \cdot 1}}{2 \cdot \frac{1}{4}}$.

Calculate the discriminant:

$b^2 - 4ac = 1 - 1 = 0$.

Since the discriminant is zero, there is exactly one real root. Substitute back into the quadratic formula:

$x = \frac{-1 \pm \sqrt{0}}{\frac{1}{2}}$.

$x = \frac{-1}{\frac{1}{2}}$.

$x = -2$.

Therefore, the solution to the equation is $x = -2$, which corresponds to choice 2.