What are the solutions to the equation (x-3)^2(3x^2-1)+16x^2=0 ?

The solutions to the equation (x-3)^2(3x^2-1)+16x^2=0 are x\approx 0.42947…,x\approx-0.48110…

Find the zeros of (x-3)^2(3x^2-1)+16x^2=0

The zeros of (x-3)^2(3x^2-1)+16x^2=0 are x\approx 0.42947…,x\approx-0.48110…

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(x - 3)^{2} (3 x^{2} - 1) + 16 x^{2} = 0

x \approx 0.42947 \dots, x \approx - 0.48110 \dots

Solution steps

(x - 3)^{2} (3 x^{2} - 1) + 16 x^{2} = 0

Expand

(x - 3)^{2} (3 x^{2} - 1) + 16 x^{2} : 3 x^{4} - 18 x^{3} + 42 x^{2} + 6 x - 9

3 x^{4} - 18 x^{3} + 42 x^{2} + 6 x - 9 = 0

Find one solution for

3 x^{4} - 18 x^{3} + 42 x^{2} + 6 x - 9 = 0

using Newton-Raphson:

x \approx 0.42947 \dots

Apply long division:

\frac{3 x ^{4} - 18 x ^{3} + 42 x ^{2} + 6 x - 9}{x - 0.42947 \dots} = 3 x^{3} - 16.71156 \dots x^{2} + 34.82273 \dots x + 20.95562 \dots

3 x^{3} - 16.71156 \dots x^{2} + 34.82273 \dots x + 20.95562 \dots \approx 0

Find one solution for

3 x^{3} - 16.71156 \dots x^{2} + 34.82273 \dots x + 20.95562 \dots = 0

using Newton-Raphson:

x \approx - 0.48110 \dots

Apply long division:

\frac{3 x ^{3} - 16.71156 \dots x ^{2} + 34.82273 \dots x + 20.95562 \dots}{x + 0.48110 \dots} = 3 x^{2} - 18.15488 \dots x + 43.55716 \dots

3 x^{2} - 18.15488 \dots x + 43.55716 \dots \approx 0

Find one solution for

3 x^{2} - 18.15488 \dots x + 43.55716 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 0.42947 \dots, x \approx - 0.48110 \dots

16 x^{4} = 15 (x + 1)^{4}

x^{4} + x^{3} + 23 x^{2} + 25 x - 50 = 0

(p) = p^{3} + 1

t^{4} - t^{2} - 2 = 0

x, 171 y = 3 x^{5}

What are the solutions to the equation (x-3)^2(3x^2-1)+16x^2=0 ?
The solutions to the equation (x-3)^2(3x^2-1)+16x^2=0 are x\approx 0.42947…,x\approx-0.48110…
Find the zeros of (x-3)^2(3x^2-1)+16x^2=0
The zeros of (x-3)^2(3x^2-1)+16x^2=0 are x\approx 0.42947…,x\approx-0.48110…