Question

5n square + 8 = -12n

Answer 1

5n² + 8 = - 12n

Add 12n to both sides to get all terms on one side of the equal sign.

5n² + 12n + 8 = 0

There are no numbers that when added together are equal to 12 but when they are multiplied together are equal to 40 so we are going to have to use the quadratic formula so solve for N.

The quadratic formula when a quadratic function is in the format ax² + bx + c = 0 is:


`x = \frac{- b +/- \sqrt{b^(2) - 4ac}}{2a}`

In this case, we are solving for N so we just place an N where then X-variable is and plug in the information from our equation:


`n = \frac{-12 +/- \sqrt{12^(2) - 4(5)(8)}}{2(5)}`

`n = (-12 +/- √(144 - 160))/(10)`

`n = (-12 +/- √(-16))/(10)`

Notice there is a negative inside of the square root. Nothing can be squared an become a negative number so we are left with an imaginary number represented by i.


`n = (-12 +/- 16i)/(10)`

Your final answer when simplified:


`n = (-6 -4i)/(5)` and
`n = (-6+4i)/(5)`