Solve the Quadratic Equation: x² - x - 20 = 0 Step-by-Step

Solve the following equation:

$x^2-x-20=0$

To solve the quadratic equation $x^2 - x - 20 = 0$ using the quadratic formula, follow these steps:

• Step 1: Identify the coefficients $a$, $b$, and $c$ in the equation. For our equation $x^2 - x - 20 = 0$, we have $a = 1$, $b = -1$, and $c = -20$.
• Step 2: Substitute these values into the quadratic formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$.
• Step 3: Calculate the discriminant $\Delta = b^2 - 4ac$:
  $\Delta = (-1)^2 - 4 \cdot 1 \cdot (-20) = 1 + 80 = 81$
• Step 4: Since the discriminant is positive, there are two distinct real roots. Substitute back into the quadratic formula:
  $x = \frac{-(-1) \pm \sqrt{81}}{2 \cdot 1} = \frac{1 \pm 9}{2}$
• Step 5: Solve for the two possible values of $x$:
  $x_1 = \frac{1 + 9}{2} = 5$ $x_2 = \frac{1 - 9}{2} = -4$

Therefore, the solutions to the equation $x^2 - x - 20 = 0$ are $x_1 = 5$ and $x_2 = -4$.

Accordingly, the correct choice matches with $x_1 = -4, x_2 = 5$, which is option 3.