Answer:
n = 6 + [tex]\sqrt{22}[/tex] or n = 6 - [tex]\sqrt{22}[/tex]
Step-by-step 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 + [tex]\sqrt{22}[/tex]
so x =6 + [tex]\sqrt{22}[/tex] or x = 6 - [tex]\sqrt{22}[/tex]
In this case x = n
n = 6 + [tex]\sqrt{22}[/tex] or n = 6 - [tex]\sqrt{22}[/tex]
Answer:
Step-by-step explanation:
The quadratic formula is [tex]\frac{-b±\sqrt{b^{2}-4ac } }{2a}[/tex]
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
[tex]n^{2} -12n+14[/tex]
So in this case, our a=1, b=-12, and c=14. Remember [tex]ax^{2}+bx+c[/tex]
So we plug these values into our formula
[tex]\frac{12±\sqrt{144-4(14)} }{2}[/tex]. Again, ignore the weird A.
simplify and you will get
[tex]\frac{12±\sqrt{88} }{2}[/tex]
simplify the square root and you get [tex]2\sqrt{22}[/tex]
divide the [tex]2\sqrt{22}[/tex] and [tex]12[/tex] by the [tex]2[/tex] on the bottom and you will get [tex]\sqrt{22}[/tex] and [tex]6[/tex]
So your answers are [tex]6-\sqrt{22}[/tex] and [tex]6+\sqrt{22}[/tex]
