Answer:
The value of n
n = 0.86
n = -0.73
Step-by-step explanation:
Given:
The given equation is
[tex]n = 2d^{2} - 5[/tex]
[tex]d = -2n[/tex]
We need to find the value of n when d = -2n.
Solution:
Rewrite the given equation as
[tex]n = 2d^{2} - 5[/tex]
Substitute d = -2n in above equation.
[tex]n = 2(-2n)^{2} - 5[/tex]
[tex]n = 2(4n^{2}) - 5[/tex]
[tex]n = 2\times 4n^{2} - 5[/tex]
[tex]n = 8n^{2} - 5[/tex]
[tex]8n^{2}-n-5=0[/tex]
Now, we first find the root of the above equation.
Use quadratic formula with [tex]a=8, b=-1, c=-5[/tex].
[tex]t=\frac{-b\pm \sqrt{(b)^{2}-4ac}}{2a}[/tex]
Put a, b and c value in above equation.
[tex]n=\frac{-(-1)\pm \sqrt{(-1)^{2}-4(8)(-5)}}{2(8)}[/tex]
[tex]n=\frac{1\pm \sqrt{1-4\times (-40)}}{16}[/tex]
[tex]n=\frac{1\pm \sqrt{1+160}}{16}[/tex]
[tex]n=\frac{1\pm \sqrt{161}}{16}[/tex]
[tex]n=\frac{1\pm 12.69}{16}[/tex]
For positive sign
[tex]n=\frac{1 + 12.69}{16}[/tex]
[tex]n=\frac{13.69}{16}[/tex]
n = 0.86
For negative sign
[tex]n=\frac{1 - 12.69}{16}[/tex]
[tex]n=\frac{-11.69}{16}[/tex]
n = -0.73
Therefore the value of n = 0.86 or n = -0.73
