What are the solutions to the equation 1/2 =4x^3-9x^2-1 ?

The solutions to the equation 1/2 =4x^3-9x^2-1 are x\approx 2.31969…

Find the zeros of 1/2 =4x^3-9x^2-1

The zeros of 1/2 =4x^3-9x^2-1 are x\approx 2.31969…

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\frac{1}{2} = 4 x^{3} - 9 x^{2} - 1

x \approx 2.31969 \dots

Solution steps

\frac{1}{2} = 4 x^{3} - 9 x^{2} - 1

Multiply both sides by

2

1 = 8 x^{3} - 18 x^{2} - 2

Switch sides

8 x^{3} - 18 x^{2} - 2 = 1

Move

1

to the left side

8 x^{3} - 18 x^{2} - 3 = 0

Find one solution for

8 x^{3} - 18 x^{2} - 3 = 0

using Newton-Raphson:

x \approx 2.31969 \dots

Apply long division:

\frac{8 x ^{3} - 18 x ^{2} - 3}{x - 2.31969 \dots} = 8 x^{2} + 0.55752 \dots x + 1.29327 \dots

8 x^{2} + 0.55752 \dots x + 1.29327 \dots \approx 0

Find one solution for

8 x^{2} + 0.55752 \dots x + 1.29327 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 2.31969 \dots

x^{3} + 9 x^{2} + 20 x = 0

x^{3} - 8 x^{2} + 5 x + 14 = 0

2 x^{4} - 2 = 0

x^{4}

x^{6} + 3 x^{2} = 0

What are the solutions to the equation 1/2 =4x^3-9x^2-1 ?
The solutions to the equation 1/2 =4x^3-9x^2-1 are x\approx 2.31969…
Find the zeros of 1/2 =4x^3-9x^2-1
The zeros of 1/2 =4x^3-9x^2-1 are x\approx 2.31969…