Solve by using tables. Give each answer to at most two decimal places.
–2x2 – 4 = –8x
To solve the equation –2x^2 – 4 = –8x using tables, we will create a table of values for both sides of the equation.
First, let's create a table for the left side of the equation, –2x^2 – 4:
|x | –2x^2 – 4 |
--------------
|-3 | –2(-3)^2 – 4 = –14 |
|-2 | –2(-2)^2 – 4 = –12 |
|-1 | –2(-1)^2 – 4 = –6 |
| 0 | –2(0)^2 – 4 = –4 |
| 1 | –2(1)^2 – 4 = –6 |
| 2 | –2(2)^2 – 4 = –12 |
| 3 | –2(3)^2 – 4 = –22 |
Now, let's create a table for the right side of the equation, –8x:
|x | –8x |
----------
|-3 | –8(-3) = 24 |
|-2 | –8(-2) = 16 |
|-1 | –8(-1) = 8 |
| 0 | –8(0) = 0 |
| 1 | –8(1) = –8 |
| 2 | –8(2) = –16 |
| 3 | –8(3) = –24 |
By examining the values in both tables, we can see that -2x^2 - 4 is not equal to -8x for any value of x. Therefore, there is no solution to the equation –2x^2 – 4 = –8x.
To solve the equation –2x^2 – 4 = –8x using tables, we will substitute different values of x into the equation and calculate the corresponding values of both sides of the equation. Then, we will look for the values of x that make the equation true.
Let's create a table to organize our calculations:
| x | -2x^2 - 4 | -8x |
|-------|-----------|-----|
| -3 | -16 | 24 |
| -2 | -12 | 16 |
| -1 | -6 | 8 |
| 0 | -4 | 0 |
| 1 | -4 | -8 |
| 2 | -8 | -16 |
| 3 | -18 | -24 |
We substitute different values of x into the equation –2x^2 – 4 = –8x and calculate the corresponding values for both sides. From the table, we can see that there are two values of x that make the equation true:
1. When x = -2, both sides of the equation have a value of 16.
2. When x = 0, both sides of the equation have a value of 0.
Therefore, the solutions to the equation –2x^2 – 4 = –8x are x = -2 and x = 0.
To solve the equation –2x^2 – 4 = –8x using tables, we can create a table of values for both sides of the equation.
First, let's rearrange the equation to bring all terms to one side:
–2x^2 + 8x - 4 = 0
Now, let's create a table with values of x and substitute them into the equation to find the corresponding values for both sides.
|x | –2x^2 + 8x - 4 |
|---|-----------------|
|0 | -4 |
|1 | 2 |
|2 | 4 |
|3 | 4 |
|4 | 0 |
|5 | -10 |
Looking at the table, we can see that the corresponding values for both sides are not the same for any value of x. Therefore, there are no solutions to the equation –2x^2 – 4 = –8x.
Since we couldn't find any solutions using the table, we can conclude that the equation has no real solutions.