x^2 + 8x -78=-5 Solve by completing the square.

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jgeertz | College Teacher | (Level 1) Associate Educator

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`x^2+8x-78=-5`

Add `78` to both sides.

`x^2+8x= 73`

In order to create a trinomial square on the left side of the equation, add a value to both sides that is equal to the square of half the coefficient of `x` . In this case, add `4^2` to both sides.

`x^2+8x+16=73+16`

`x^2+8x+16=89`

Now factor the perfect trinomial square.

`(x+4)^2 =89`

Take the square root of each side of the equation.

`(x+4)^(2/2) = +-sqrt89`

`x+4 =+-sqrt89`

`x= +sqrt89 -4`

`x=-sqrt89 -4` 

The complete solution is:

`x=sqrt89 - 4, -sqrt89-4`

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