# How do you solve #9x^2 - 7x = 12# using completing the square?

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To solve the equation (9x^2 - 7x = 12) using completing the square:

- Move the constant term to the other side: (9x^2 - 7x - 12 = 0).
- Divide all terms by the coefficient of (x^2): (x^2 - \frac{7}{9}x - \frac{4}{3} = 0).
- To complete the square, take half of the coefficient of (x) ((-\frac{7}{9})), square it, and add it to both sides of the equation: (x^2 - \frac{7}{9}x + \left(\frac{7}{18}\right)^2 - \left(\frac{7}{18}\right)^2 - \frac{4}{3} = 0).
- Simplify: (x^2 - \frac{7}{9}x + \frac{49}{324} - \frac{49}{324} - \frac{4}{3} = 0).
- Combine like terms: (x^2 - \frac{7}{9}x + \frac{49}{324} - \frac{196}{324} = 0).
- Factor the perfect square trinomial and simplify: (\left(x - \frac{7}{18}\right)^2 - \frac{245}{324} = 0).
- Add (\frac{245}{324}) to both sides: (\left(x - \frac{7}{18}\right)^2 = \frac{245}{324}).
- Take the square root of both sides: (x - \frac{7}{18} = \pm \sqrt{\frac{245}{324}}).
- Solve for (x): (x = \frac{7}{18} \pm \sqrt{\frac{245}{324}}).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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