What are the solutions to the equation (x+2)^2(2x-5)/3 =3 ?

The solutions to the equation (x+2)^2(2x-5)/3 =3 are x\approx 2.70341…

Find the zeros of (x+2)^2(2x-5)/3 =3

The zeros of (x+2)^2(2x-5)/3 =3 are x\approx 2.70341…

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(x + 2)^{2} \frac{2 x - 5}{3} = 3

x \approx 2.70341 \dots

Solution steps

(x + 2)^{2} \frac{2 x - 5}{3} = 3

Expand

(x + 2)^{2} \frac{2 x - 5}{3} : \frac{2 x ^{3}}{3} + x^{2} - 4 x - \frac{20}{3}

\frac{2 x ^{3}}{3} + x^{2} - 4 x - \frac{20}{3} = 3

Move

3

to the left side

\frac{2 x ^{3} - 20}{3} + x^{2} - 4 x - 3 = 0

Write in the standard form

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

\frac{2 x ^{3}}{3} + x^{2} - 4 x - \frac{20}{3} - 3 = 0

Find one solution for

0.66666 \dots x^{3} + x^{2} - 4 x - 9.66666 \dots = 0

using Newton-Raphson:

x \approx 2.70341 \dots

Apply long division:

\frac{\frac{2 x ^{3}}{3} + x ^{2} - 4 x - \frac{20}{3} - 3}{x - 2.70341 \dots} = 0.66666 \dots x^{2} + 2.80227 \dots x + 3.57572 \dots

0.66666 \dots x^{2} + 2.80227 \dots x + 3.57572 \dots \approx 0

Find one solution for

0.66666 \dots x^{2} + 2.80227 \dots x + 3.57572 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 2.70341 \dots

5 x^{6} - (3 - 2 x) 8 = (4 x - 3) 12

x^{3} - 6 x^{2} - 15 x + 90 = 0

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

3 x^{3} + 9 x^{2} + 8 x = 0

2 x^{3} - 7 x^{2} + x + 10 = 0

What are the solutions to the equation (x+2)^2(2x-5)/3 =3 ?
The solutions to the equation (x+2)^2(2x-5)/3 =3 are x\approx 2.70341…
Find the zeros of (x+2)^2(2x-5)/3 =3
The zeros of (x+2)^2(2x-5)/3 =3 are x\approx 2.70341…