Question

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

Answer 1

The value of n

n = 0.86

n = -0.73

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* 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=(1\pm √(1-4* (-40)))/(16)`

`n=(1\pm √(1+160))/(16)`

`n=(1\pm √(161))/(16)`

`n=(1\pm 12.69)/(16)`

For positive sign

`n=(1 + 12.69)/(16)`

`n=(13.69)/(16)`

n = 0.86

For negative sign

`n=(1 - 12.69)/(16)`

`n=(-11.69)/(16)`

n = -0.73

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