The problem is to solve the quadratic equation $x^2 - 4x - 21 = 0$.

1. Problem Description

The problem is to solve the quadratic equation $x^2 - 4x - 21 = 0$.

2. Solution Steps

We can solve this quadratic equation by factoring. We are looking for two numbers that multiply to -21 and add up to -

4. These numbers are -7 and

3. Therefore, we can rewrite the quadratic equation as follows:

$(x - 7)(x + 3) = 0$

Now, we set each factor equal to zero and solve for $x$:

$x - 7 = 0$ or $x + 3 = 0$

Solving for $x$ in each case:

$x = 7$ or $x = -3$

3. Final Answer

The solutions to the equation $x^2 - 4x - 21 = 0$ are $x = 7$ and $x = -3$.