SOLUTION: solve equation by completing the square n^2+16n-97=-3

Question 201572: solve equation by completing the square
n^2+16n-97=-3
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation.

Add 3 to both sides.

Combine like terms.

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Now let's complete the square for the expression

Start with the given expression.

Take half of the coefficient to get . In other words, .

Now square to get . In other words,

Now add and subtract . Make sure to place this after the "n" term. Notice how . So the expression is not changed.

Group the first three terms.

Factor to get .

Combine like terms.

So after completing the square, transforms to . So .

So is equivalent to .

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Now let's solve

Start with the given equation.

Add to both sides.

Combine like terms.

Take the square root of both sides.

or Break up the "plus/minus" to form two equations.

or Subtract from both sides.

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Answer:

So the solutions are or .
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