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umka21 [38]
3 years ago
12

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

Mathematics
1 answer:
alekssr [168]3 years ago
4 0

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

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