What are the solutions to the equation 26.28=0.15x^3+0.3x^2 ?

The solutions to the equation 26.28=0.15x^3+0.3x^2 are x\approx 5.00210…

Find the zeros of 26.28=0.15x^3+0.3x^2

The zeros of 26.28=0.15x^3+0.3x^2 are x\approx 5.00210…

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26.28 = 0.15 x^{3} + 0.3 x^{2}

x \approx 5.00210 \dots

Solution steps

26.28 = 0.15 x^{3} + 0.3 x^{2}

Multiply both sides by

100

2628 = 15 x^{3} + 30 x^{2}

Switch sides

15 x^{3} + 30 x^{2} = 2628

Move

2628

to the left side

15 x^{3} + 30 x^{2} - 2628 = 0

Find one solution for

15 x^{3} + 30 x^{2} - 2628 = 0

using Newton-Raphson:

x \approx 5.00210 \dots

Apply long division:

\frac{15 x ^{3} + 30 x ^{2} - 2628}{x - 5.00210 \dots} = 15 x^{2} + 105.03156 \dots x + 525.37887 \dots

15 x^{2} + 105.03156 \dots x + 525.37887 \dots \approx 0

Find one solution for

15 x^{2} + 105.03156 \dots x + 525.37887 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 5.00210 \dots

x^{3} + 4 x^{2} + x + 4

x^{3} + x^{2} - x - 1

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

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

x^{4} + 14 x^{3} + 77 x^{2} + 200 x + 208 = 0

What are the solutions to the equation 26.28=0.15x^3+0.3x^2 ?
The solutions to the equation 26.28=0.15x^3+0.3x^2 are x\approx 5.00210…
Find the zeros of 26.28=0.15x^3+0.3x^2
The zeros of 26.28=0.15x^3+0.3x^2 are x\approx 5.00210…