Question

Solve the equation using a table.
x^2 - 13x + 40 = 0

Answer 1

To solve the quadratic equation x^2 - 13x + 40 = 0 using a table, we can follow these steps:

1. Create a table with three columns labeled "x", "x^2", and "x^2 - 13x + 40".

|x | x^2 | x^2 - 13x + 40 |
|---|-----|--------------|
| -5 | 25 | 125 |
| -4 | 16 | 96 |
| -3 | 9 | 61 |
| -2 | 4 | 36 |
| -1 | 1 | 25 |
| 0 | 0 | 40 |
| 1 | 1 | 28 |
| 2 | 4 | 16 |
| 3 | 9 | 7 |
| 4 | 16 | 0 |
| 5 | 25 | -15 |

2. Fill in the first column of the table with different values for x.
3. Calculate the corresponding values for x^2 and x^2 - 13x + 40.
4. Look for any rows where the value of x^2 - 13x + 40 is equal to 0.
5. In this case, we see that when x = 4, the value of x^2 - 13x + 40 is 0.
6. Therefore, the solution to the quadratic equation x^2 - 13x + 40 = 0 is x = 4.