The given equation is a quadratic equation. Here's how to solve it step-by-step.
1. The given equation is of the form: "x^2 - x - 20 = 0".
2. First, we rearrange the equation and set it equal to zero: x^2 - x - 20 = 0.
3. Next, we factor the equation (break the equation down into its simplest terms or into an equation that is easier to solve). By looking at the equation, we can factor it into two binomial equations. We are looking for two numbers that multiply to -20 and add up to -1 (the coefficient of x). Those numbers are -5 and 4. Therefore, we factor the equation into (x-5)*(x+4) = 0.
4. We then set each factor equal to zero and solve for x.
5. If we set the first factor (x - 5) equal to zero, we get:
x - 5 = 0;
Add 5 to both sides;
x = 5.
6. If we set the second factor (x + 4) equal to zero, we get:
x + 4 = 0;
Subtract 4 from both sides;
x = -4.
So, the solutions for the given quadratic equation x^2 - x - 20 = 0 are x = -4, 5.