What are the solutions to the equation 0.1n^2+100n+8=1000 ?

The solutions to the equation 0.1n^2+100n+8=1000 are n=4(57sqrt(5)-125),n=-4(125+57sqrt(5))

Find the zeros of 0.1n^2+100n+8=1000

The zeros of 0.1n^2+100n+8=1000 are n=4(57sqrt(5)-125),n=-4(125+57sqrt(5))

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0.1 n^{2} + 100 n + 8 = 1000

n = 4 (575 - 125), n = - 4 (125 + 575)

Solution steps

0.1 n^{2} + 100 n + 8 = 1000

Multiply both sides by

10

n^{2} + 1000 n + 80 = 10000

Move

10000

to the left side

n^{2} + 1000 n - 9920 = 0

Solve with the quadratic formula

n_{1, 2} = \frac{- 1000 \pm 100 0 ^{2} - 4 \cdot 1 \cdot ( - 9920 )}{2 \cdot 1}

100 0^{2} - 4 \cdot 1 \cdot (- 9920) = 4565

n_{1, 2} = \frac{- 1000 \pm 456 5}{2 \cdot 1}

Separate the solutions

n_{1} = \frac{- 1000 + 456 5}{2 \cdot 1}, n_{2} = \frac{- 1000 - 456 5}{2 \cdot 1}

n = \frac{- 1000 + 456 5}{2 \cdot 1} : 4 (575 - 125)

n = \frac{- 1000 - 456 5}{2 \cdot 1} : - 4 (125 + 575)

The solutions to the quadratic equation are:

n = 4 (575 - 125), n = - 4 (125 + 575)

- 8 x^{2} + 48 x + 576 = 0

x^{2} + 82 x + 1681 = 0

x^{2} + 5 x + 2 = - 4

- x^{2} - 5 x + 25 = - 2 x^{2} + 5 x

16 x^{2} - 24 x + 7 = 0

What are the solutions to the equation 0.1n^2+100n+8=1000 ?
The solutions to the equation 0.1n^2+100n+8=1000 are n=4(57sqrt(5)-125),n=-4(125+57sqrt(5))
Find the zeros of 0.1n^2+100n+8=1000
The zeros of 0.1n^2+100n+8=1000 are n=4(57sqrt(5)-125),n=-4(125+57sqrt(5))