Question

N² + 14 = 12n
how do I solve by quadratic formula ​

Answer 1

Explanation:

The quadratic formula is
`\frac{-b±\sqrt{b^(2)-4ac } }{2a}`

Ignore the weird A at the beginning, I don't know why it is there.

To get your equation into a quadratic equation, we have to move 12n to the other side, giving us

`n^(2) -12n+14`

So in this case, our a=1, b=-12, and c=14. Remember
`ax^(2)+bx+c`

So we plug these values into our formula

`(12±√(144-4(14)) )/(2)`. Again, ignore the weird A.

simplify and you will get

`(12±√(88) )/(2)`

simplify the square root and you get
`2√(22)`

divide the
`2√(22)` and
`12` by the
`2` on the bottom and you will get
`√(22)` and
`6`

So your answers are
`6-√(22)` and
`6+√(22)`

Answer 2

n = 6 +
`√(22)` or n = 6 -
`√(22)`

Explanation:

We can solve this equation using the quadratic formula OR Completing the Square method.

n² + 14 = 12n

rearrange : n² - 12n + 14 = 0

here a= 1 , b = -12, c = 14

the quadratic formula says: x = - b/ (2a) + root(b^2 - 4ac) / (2a)

or x = - b/ (2a) - root(b^2 - 4ac) / (2a)

x = - (-12)/ (2) + root((-12)^2 - 4*14) / (2)

x = 6 + root (144 - 56) / 2

x = 6 + root(88)/2

x = 6 + root(4*22) / 2

x = 6 + 2*root(22)/2

x = 6 + root(22) = 6 +
`√(22)`

so x =6 +
`√(22)` or x = 6 -
`√(22)`

In this case x = n

n = 6 +
`√(22)` or n = 6 -
`√(22)`