What are the solutions to the equation 5x^1+10x^2+15x^3=50 ?

The solutions to the equation 5x^1+10x^2+15x^3=50 are x\approx 1.23822…

Find the zeros of 5x^1+10x^2+15x^3=50

The zeros of 5x^1+10x^2+15x^3=50 are x\approx 1.23822…

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5 x^{1} + 10 x^{2} + 15 x^{3} = 50

x \approx 1.23822 \dots

Solution steps

5 x^{1} + 10 x^{2} + 15 x^{3} = 50

Refine

5 x + 10 x^{2} + 15 x^{3} = 50

Move

50

to the left side

5 x + 10 x^{2} + 15 x^{3} - 50 = 0

Write in the standard form

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

15 x^{3} + 10 x^{2} + 5 x - 50 = 0

Find one solution for

15 x^{3} + 10 x^{2} + 5 x - 50 = 0

using Newton-Raphson:

x \approx 1.23822 \dots

Apply long division:

\frac{15 x ^{3} + 10 x ^{2} + 5 x - 50}{x - 1.23822 \dots} = 15 x^{2} + 28.57339 \dots x + 40.38033 \dots

15 x^{2} + 28.57339 \dots x + 40.38033 \dots \approx 0

Find one solution for

15 x^{2} + 28.57339 \dots x + 40.38033 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 1.23822 \dots

2 x^{4} = 432 x

x^{5} - 80 x + 50 = 0

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

w^{3} - 2 w^{2} + w - 2 = 0.2

- 4 x^{5} + 32 x^{3} + 192 x = 0

What are the solutions to the equation 5x^1+10x^2+15x^3=50 ?
The solutions to the equation 5x^1+10x^2+15x^3=50 are x\approx 1.23822…
Find the zeros of 5x^1+10x^2+15x^3=50
The zeros of 5x^1+10x^2+15x^3=50 are x\approx 1.23822…