What are the solutions to the equation x^2(2x+3)=35 ?

The solutions to the equation x^2(2x+3)=35 are x\approx 2.18053…

Find the zeros of x^2(2x+3)=35

The zeros of x^2(2x+3)=35 are x\approx 2.18053…

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x^{2} (2 x + 3) = 35

x \approx 2.18053 \dots

Solution steps

x^{2} (2 x + 3) = 35

Expand

x^{2} (2 x + 3) : 2 x^{3} + 3 x^{2}

2 x^{3} + 3 x^{2} = 35

Move

35

to the left side

2 x^{3} + 3 x^{2} - 35 = 0

Find one solution for

2 x^{3} + 3 x^{2} - 35 = 0

using Newton-Raphson:

x \approx 2.18053 \dots

Apply long division:

\frac{2 x ^{3} + 3 x ^{2} - 35}{x - 2.18053 \dots} = 2 x^{2} + 7.36107 \dots x + 16.05109 \dots

2 x^{2} + 7.36107 \dots x + 16.05109 \dots \approx 0

Find one solution for

2 x^{2} + 7.36107 \dots x + 16.05109 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 2.18053 \dots

(3 x - 2) (x + 1)^{2} (3 x + 8) = 16

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

(x^{2} + x) (x^{2} - x) = (x - 2)^{2} + x (x + 4)

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

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

What are the solutions to the equation x^2(2x+3)=35 ?
The solutions to the equation x^2(2x+3)=35 are x\approx 2.18053…
Find the zeros of x^2(2x+3)=35
The zeros of x^2(2x+3)=35 are x\approx 2.18053…