Question

For n = 2d squared - 5 when d = -2nwhat does n equal

Answer 1

Answer:

The value of n

n = 0.86

n = -0.73

Step-by-step explanation:

Given:

The given equation is

$n = 2d^{2} - 5$

$d = -2n$

We need to find the value of n when d = -2n.

Solution:

Rewrite the given equation as

$n = 2d^{2} - 5$

Substitute d = -2n in above equation.

$n = 2(-2n)^{2} - 5$

$n = 2(4n^{2}) - 5$

$n = 2\times 4n^{2} - 5$

$n = 8n^{2} - 5$

$8n^{2}-n-5=0$

Now, we first find the root of the above equation.

Use quadratic formula with $a=8, b=-1, c=-5$.

$t=\frac{-b\pm \sqrt{(b)^{2}-4ac}}{2a}$

Put a, b and c value in above equation.

$n=\frac{-(-1)\pm \sqrt{(-1)^{2}-4(8)(-5)}}{2(8)}$

$n=\frac{1\pm \sqrt{1-4\times (-40)}}{16}$

$n=\frac{1\pm \sqrt{1+160}}{16}$

$n=\frac{1\pm \sqrt{161}}{16}$

$n=\frac{1\pm 12.69}{16}$

For positive sign

$n=\frac{1 + 12.69}{16}$

$n=\frac{13.69}{16}$

n = 0.86

For negative sign

$n=\frac{1 - 12.69}{16}$

$n=\frac{-11.69}{16}$

n = -0.73

Therefore the value of n = 0.86 or n = -0.73