What are the solutions to the equation s(2s+0.1)^2=8*10^{-9} ?

The solutions to the equation s(2s+0.1)^2=8*10^{-9} are s\approx 0.00000…,s\approx-0.04999…,s=-1/20

Find the zeros of s(2s+0.1)^2=8*10^{-9}

The zeros of s(2s+0.1)^2=8*10^{-9} are s\approx 0.00000…,s\approx-0.04999…,s=-1/20

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s (2 s + 0.1)^{2} = 8 \cdot 1 0^{- 9}

s \approx 0.00000 \dots, s \approx - 0.04999 \dots, s = - \frac{1}{20}

Decimal Notation

s = 0, s = - 0.04999 \dots, s = - 0.05

Solution steps

s (2 s + 0.1)^{2} = 8 \cdot 1 0^{- 9}

Expand

s (2 s + 0.1)^{2} : 4 s^{3} + 0.4 s^{2} + 0.01 s

Expand

8 \cdot 1 0^{- 9} : \frac{1}{125000000}

4 s^{3} + 0.4 s^{2} + 0.01 s = \frac{1}{125000000}

Move

\frac{1}{125000000}

to the left side

4 s^{3} + 0.4 s^{2} + 0.01 s - 0.000000008 = 0

Find one solution for

4 s^{3} + 0.4 s^{2} + 0.01 s = 0

using Newton-Raphson:

s \approx 0.00000 \dots

Apply long division:

\frac{4 s ^{3} + 0.4 s ^{2} + 0.01 s - 0.000000008}{s} = 4 s^{2} + 0.4 s + 0.01

4 s^{2} + 0.4 s + 0.01 \approx 0

Find one solution for

4 s^{2} + 0.4 s + 0.01 = 0

using Newton-Raphson:

s \approx - 0.04999 \dots

Apply long division:

\frac{4 s ^{2} + 0.4 s + 0.01}{s + 0.04999 \dots} = 4 s + 0.20000 \dots

4 s + 0.20000 \dots \approx 0

s \approx - 0.05000 \dots

Approximate to algebraic form

s = - \frac{1}{20}

The solutions are

s \approx 0, s \approx - 0.04999 \dots, s = - \frac{1}{20}

3 x^{3} - x - 10 x = - x^{2} + 2 x

x^{4} - a^{4} = 0

x^{3} - 4 = 60

a (a^{2} - 2 a) = 0

x, x (x + 1) (x + 2) = - 1

What are the solutions to the equation s(2s+0.1)^2=8*10^{-9} ?
The solutions to the equation s(2s+0.1)^2=8*10^{-9} are s\approx 0.00000…,s\approx-0.04999…,s=-1/20
Find the zeros of s(2s+0.1)^2=8*10^{-9}
The zeros of s(2s+0.1)^2=8*10^{-9} are s\approx 0.00000…,s\approx-0.04999…,s=-1/20