What are the solutions to the equation x^2(25-4x)=5 ?

The solutions to the equation x^2(25-4x)=5 are x\approx-0.43249…,x\approx 0.46483…,x\approx 6.21766…

Find the zeros of x^2(25-4x)=5

The zeros of x^2(25-4x)=5 are x\approx-0.43249…,x\approx 0.46483…,x\approx 6.21766…

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x^{2} (25 - 4 x) = 5

x \approx - 0.43249 \dots, x \approx 0.46483 \dots, x \approx 6.21766 \dots

Solution steps

x^{2} (25 - 4 x) = 5

Expand

x^{2} (25 - 4 x) : 25 x^{2} - 4 x^{3}

25 x^{2} - 4 x^{3} = 5

Move

5

to the left side

25 x^{2} - 4 x^{3} - 5 = 0

Write in the standard form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

- 4 x^{3} + 25 x^{2} - 5 = 0

Find one solution for

- 4 x^{3} + 25 x^{2} - 5 = 0

using Newton-Raphson:

x \approx - 0.43249 \dots

Apply long division:

\frac{- 4 x ^{3} + 25 x ^{2} - 5}{x + 0.43249 \dots} = - 4 x^{2} + 26.72999 \dots x - 11.56070 \dots

- 4 x^{2} + 26.72999 \dots x - 11.56070 \dots \approx 0

Find one solution for

- 4 x^{2} + 26.72999 \dots x - 11.56070 \dots = 0

using Newton-Raphson:

x \approx 0.46483 \dots

Apply long division:

\frac{- 4 x ^{2} + 26.72999 \dots x - 11.56070 \dots}{x - 0.46483 \dots} = - 4 x + 24.87066 \dots

- 4 x + 24.87066 \dots \approx 0

x \approx 6.21766 \dots

The solutions are

x \approx - 0.43249 \dots, x \approx 0.46483 \dots, x \approx 6.21766 \dots

x^{3} = 64000

2 x^{3} + 5 x^{2} - 12 x = 0

2 x^{3} - 17 x^{2} - 11 x - 1 = 0

y^{4} + 32 y^{2} - 144 = 0

x^{3} - 5 x^{2} + 12 = 0

What are the solutions to the equation x^2(25-4x)=5 ?
The solutions to the equation x^2(25-4x)=5 are x\approx-0.43249…,x\approx 0.46483…,x\approx 6.21766…
Find the zeros of x^2(25-4x)=5
The zeros of x^2(25-4x)=5 are x\approx-0.43249…,x\approx 0.46483…,x\approx 6.21766…