What are the solutions to the equation (2+h)^3-9(2)h=0.1 ?

The solutions to the equation (2+h)^3-9(2)h=0.1 are h\approx-7.01572…

Find the zeros of (2+h)^3-9(2)h=0.1

The zeros of (2+h)^3-9(2)h=0.1 are h\approx-7.01572…

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(2 + h)^{3} - 9 (2) h = 0.1

h \approx - 7.01572 \dots

Solution steps

(2 + h)^{3} - 9 (2) h = 0.1

Multiply both sides by

10

10 (2 + h)^{3} - 180 h = 1

Expand

10 (2 + h)^{3} - 180 h : 10 h^{3} + 60 h^{2} - 60 h + 80

10 h^{3} + 60 h^{2} - 60 h + 80 = 1

Move

1

to the left side

10 h^{3} + 60 h^{2} - 60 h + 79 = 0

Find one solution for

10 h^{3} + 60 h^{2} - 60 h + 79 = 0

using Newton-Raphson:

h \approx - 7.01572 \dots

Apply long division:

\frac{10 h ^{3} + 60 h ^{2} - 60 h + 79}{h + 7.01572 \dots} = 10 h^{2} - 10.15724 \dots h + 11.26041 \dots

10 h^{2} - 10.15724 \dots h + 11.26041 \dots \approx 0

Find one solution for

10 h^{2} - 10.15724 \dots h + 11.26041 \dots = 0

using Newton-Raphson:

No Solution for

h \in R

The solution is

h \approx - 7.01572 \dots

D^{4} + 2 D^{3} - 11 D^{2} - 12 D = 0

x, x^{3} - y^{5} = 0

4 (5 x^{9}) = 5

x^{6} + 6 x^{4} + 9 x^{2} + 4 = 0

y^{4} - 26 y^{2} + 25 = 0

What are the solutions to the equation (2+h)^3-9(2)h=0.1 ?
The solutions to the equation (2+h)^3-9(2)h=0.1 are h\approx-7.01572…
Find the zeros of (2+h)^3-9(2)h=0.1
The zeros of (2+h)^3-9(2)h=0.1 are h\approx-7.01572…