SOLUTION: solve for x using the factoring method: 18x^3=2x

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Question 228522: solve for x using the factoring method: 18x^3=2x
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x using the factoring method: 18x%5E3=2x

Step 1. Subtract 2x from both sides of the equation

18x%5E3-2x=2x-2x

18x%5E3-2x=0

Step 2. Look at the numbers which has 2 as a common factor. Then,

2%289x%5E3-x%29=0

Step 3. Look at the variable x which has x as a common factor. Then,

2x%289x%5E2-1%29=0.

Step 4. But 9x%5E2-1=9x%5E2-1%5E2=%283x-1%29%283x%2B1%29 which is recognized as the difference of squares. As a result we have,

2x%289x%5E2-1%29=2x%283x-1%29%283x%2B1%29=0

Step 5. This implies x=0, 3x-1=0 and 3x%2B1=0.

Add 1 to both sides of 3x-1=0 to get 3x=1.

Divide by 3 to both sides of the equation to get x=1%2F3

Subtract 1 to both sides of 3x%2B1=0 to get 3x=-1

Divide by 3 to both sides of the equation to get x=-1%2F3

Step 6. ANSWER: The solution is x=0, x=-1%2F3 and x=1%2F3.

I hope the above steps were helpful.

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Good luck in your studies!

Respectfully,
Dr J