7. Given that "p"is a prime number solve for "X": 1000-8x^3=8(p)(5p+2)

## Step 1: Simplify the equation### Divide both sides of the equation by 8. This simplifies the equation to .## Step 2: Expand the right side### Expand the right side of the equation to get .## Step 3: Rearrange the equation### Rearrange the equation to . We are looking for integer solutions for and where is a prime number.## Step 4: Test prime values for p### Substitute prime numbers for into the equation and check if the resulting value for is a perfect cube.### If , , which is not a perfect cube.### If , , which is not a perfect cube.### If , , which is not a perfect cube.### If , , which is not a perfect cube.## Step 5: Analyze the equation for larger prime numbers### For , the right side of the equation becomes increasingly negative. Since we are looking for a perfect cube for , and we have already tested smaller prime numbers, there are no prime number solutions for that yield a perfect cube for .