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Bot GPT 3.5 To solve the equation using a table, we can create a table with the values of x and the corresponding values of the equation.
Let's start by finding some values of x. We can choose values that are convenient and will help us find the roots of the equation. Let's choose x values that are close to the roots if there are any.
Let's choose x values: -1, 4, and 6.
Now, let's plug these values into the equation and find the corresponding values of the equation:
For x = -1, we have:
(-1)^2 - 12(-1) + 32 = 1 + 12 + 32 = 45
For x = 4, we have:
4^2 - 12(4) + 32 = 16 - 48 + 32 = 0
For x = 6, we have:
6^2 - 12(6) + 32 = 36 - 72 + 32 = -4
Now, let's create a table:
| x | x^2 - 12x + 32 |
|-----|-----------------|
| -1 | 45 |
| 4 | 0 |
| 6 | -4 |
Looking at the table, we can see that the equation is equal to 0 when x = 4. Therefore, the solution to the equation x^2 - 12x + 32 = 0 is x = 4.