What are the solutions to the equation 35=(x^2(4x+6))/2 ?

The solutions to the equation 35=(x^2(4x+6))/2 are x\approx 2.18053…

Find the zeros of 35=(x^2(4x+6))/2

The zeros of 35=(x^2(4x+6))/2 are x\approx 2.18053…

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35 = \frac{x ^{2} ( 4 x + 6 )}{2}

x \approx 2.18053 \dots

Solution steps

35 = \frac{x ^{2} ( 4 x + 6 )}{2}

Multiply both sides by

2

70 = x^{2} (4 x + 6)

Expand

x^{2} (4 x + 6) : 4 x^{3} + 6 x^{2}

70 = 4 x^{3} + 6 x^{2}

Switch sides

4 x^{3} + 6 x^{2} = 70

Move

70

to the left side

4 x^{3} + 6 x^{2} - 70 = 0

Find one solution for

4 x^{3} + 6 x^{2} - 70 = 0

using Newton-Raphson:

x \approx 2.18053 \dots

Apply long division:

\frac{4 x ^{3} + 6 x ^{2} - 70}{x - 2.18053 \dots} = 4 x^{2} + 14.72214 \dots x + 32.10218 \dots

4 x^{2} + 14.72214 \dots x + 32.10218 \dots \approx 0

Find one solution for

4 x^{2} + 14.72214 \dots x + 32.10218 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 2.18053 \dots

22 = 3 (x + 3)^{3} - 2

2 x^{3} - 13 x^{2} + 22 x - 8 = 0

x, y = x^{3} + 3

0 = x^{3} - 6 x^{2} + 32

x, y = x^{3} - 1

What are the solutions to the equation 35=(x^2(4x+6))/2 ?
The solutions to the equation 35=(x^2(4x+6))/2 are x\approx 2.18053…
Find the zeros of 35=(x^2(4x+6))/2
The zeros of 35=(x^2(4x+6))/2 are x\approx 2.18053…