Question

How many solutions can be found for the linear equation?

3(x2
+ 5) - 6 = (9x+18)3

Answer 1

Then solve it

Answer 2

To find how many solutions can be found for the linear equation, we need to simplify it first:

3(x^2 + 5) - 6 = (9x + 18)^3

Next, we can expand both sides of the equation:

3x^2 + 15 - 6 = 729x^3 + 1458x^2 + 972x + 324

Combining like terms:

3x^2 + 9 = 729x^3 + 1458x^2 + 972x + 324

Now, this equation is a cubic equation, so it can have up to 3 solutions. However, we'd need to solve it to determine the actual number of solutions.

Answer 3

To solve the cubic equation:

3x^2 + 9 = 729x^3 + 1458x^2 + 972x + 324

Firstly, let's move all terms to one side to get a zero on the other side:

729x^3 + 1458x^2 + 972x + 324 - 3x^2 - 9 = 0

Simplifying:

729x^3 + 1455x^2 + 972x + 315 = 0

Unfortunately, the equation does not factor easily. So, we will need to use numerical methods or a calculator to find the solutions.