What are the solutions to the equation 4x^3-6x^2-3= 1/2 ?

The solutions to the equation 4x^3-6x^2-3= 1/2 are x\approx 1.77707…

Find the zeros of 4x^3-6x^2-3= 1/2

The zeros of 4x^3-6x^2-3= 1/2 are x\approx 1.77707…

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4 x^{3} - 6 x^{2} - 3 = \frac{1}{2}

x \approx 1.77707 \dots

Solution steps

4 x^{3} - 6 x^{2} - 3 = \frac{1}{2}

Multiply both sides by

2

8 x^{3} - 12 x^{2} - 6 = 1

Move

1

to the left side

8 x^{3} - 12 x^{2} - 7 = 0

Find one solution for

8 x^{3} - 12 x^{2} - 7 = 0

using Newton-Raphson:

x \approx 1.77707 \dots

Apply long division:

\frac{8 x ^{3} - 12 x ^{2} - 7}{x - 1.77707 \dots} = 8 x^{2} + 2.21659 \dots x + 3.93905 \dots

8 x^{2} + 2.21659 \dots x + 3.93905 \dots \approx 0

Find one solution for

8 x^{2} + 2.21659 \dots x + 3.93905 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 1.77707 \dots

x^{4} - 4 x^{2} - 45 = 0

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

x^{3} - 14 x^{2} + 59 x - 70 = 0

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

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

What are the solutions to the equation 4x^3-6x^2-3= 1/2 ?
The solutions to the equation 4x^3-6x^2-3= 1/2 are x\approx 1.77707…
Find the zeros of 4x^3-6x^2-3= 1/2
The zeros of 4x^3-6x^2-3= 1/2 are x\approx 1.77707…