How do you write #5n^2+19n-68=-2# into vertex form?

Answer 1
#5n^2+19n-68=-2# to be written in the form: #m(n-a)^2+b = 0#

Take the constant out of the working left side for the time being.

#5n^2+19n = 66#
Extract the #m (=5)# factor
#5(n^2+19/5n) = 66#

Finish the square.

#5(n^2+19/5n+(19/10)^2) = 66 + 5(19/10)^2#
#5(n+19/10)^2 = 66 + 361/20 = 1681/20#

To finish the vertex form, move the constant back to the left:

#5(n+19/10)^2 - 1681/20 = 0# or #5(n-(-19/10))^2 +(- 1681/20) = 0#
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Answer 2

To write the quadratic equation (5n^2 + 19n - 68 = -2) into vertex form, follow these steps:

  1. Rewrite the equation in standard form: (5n^2 + 19n - 66 = 0).
  2. Factor out the leading coefficient (a): (5(n^2 + \frac{19}{5}n) - 66 = 0).
  3. Complete the square inside the parentheses: (5(n^2 + \frac{19}{5}n + (\frac{19}{10})^2) - 66 - 5(\frac{19}{10})^2 = 0).
  4. Simplify inside the parentheses: (5(n^2 + \frac{19}{5}n + \frac{361}{100}) - 66 - \frac{361}{4} = 0).
  5. Rewrite the constant term: (5(n^2 + \frac{19}{5}n + \frac{361}{100}) - \frac{2644}{25} = 0).
  6. Rewrite the constant term as a perfect square: (5(n + \frac{19}{10})^2 - \frac{2644}{25} = 0).
  7. Move the constant term to the other side: (5(n + \frac{19}{10})^2 = \frac{2644}{25}).
  8. Divide both sides by the leading coefficient (a): (n + \frac{19}{10})^2 = \frac{2644}{125}).
  9. The vertex form is (n + \frac{19}{10})^2 = \frac{2644}{125}).
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Answer from HIX Tutor

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.

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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