Solve the Quadratic Equation: x²/4 + x - 1¼ = 0

To solve this quadratic equation, we'll follow these steps:

• Step 1: Eliminate fractions and rearrange the equation.
• Step 2: Use the Quadratic Formula to find the solutions.
• Step 3: Simplify the solutions for $x$.

Now, let's work through each step:

Step 1: The given equation is $\frac{x^2}{4} + x - 1\frac{1}{4} = 0$.

First, multiply every term by 4 to eliminate the fraction: $x^2 + 4x - 5 = 0$

Step 2: The equation is now in the standard form $ax^2 + bx + c = 0$ with $a = 1$, $b = 4$, and $c = -5$.

Step 3: Apply the Quadratic Formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

Substitute the values of $a$, $b$, and $c$: $x = \frac{-4 \pm \sqrt{4^2 - 4 \times 1 \times (-5)}}{2 \times 1}$ $x = \frac{-4 \pm \sqrt{16 + 20}}{2}$ $x = \frac{-4 \pm \sqrt{36}}{2}$

Simplify the square root and solve for $x$: $x = \frac{-4 \pm 6}{2}$

Calculating the two possible solutions: $x_1 = \frac{-4 + 6}{2} = \frac{2}{2} = 1$ $x_2 = \frac{-4 - 6}{2} = \frac{-10}{2} = -5$

Therefore, the solutions to the quadratic equation are $x_1 = 1$ and $x_2 = -5$.

The correct choice corresponds to the answer: $x_1 = 1, x_2 = -5$.