What are the solutions to the equation x=6.9+9(x-5)^3 ?

The solutions to the equation x=6.9+9(x-5)^3 are x\approx 4.34256…

Find the zeros of x=6.9+9(x-5)^3

The zeros of x=6.9+9(x-5)^3 are x\approx 4.34256…

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x = 6.9 + 9 (x - 5)^{3}

x \approx 4.34256 \dots

Solution steps

x = 6.9 + 9 (x - 5)^{3}

Multiply both sides by

10

x \cdot 10 = 69 + 90 (x - 5)^{3}

Expand

69 + 90 (x - 5)^{3} : 90 x^{3} - 1350 x^{2} + 6750 x - 11181

x \cdot 10 = 90 x^{3} - 1350 x^{2} + 6750 x - 11181

Switch sides

90 x^{3} - 1350 x^{2} + 6750 x - 11181 = x \cdot 10

Move

x 10

to the left side

90 x^{3} - 1350 x^{2} + 6740 x - 11181 = 0

Find one solution for

90 x^{3} - 1350 x^{2} + 6740 x - 11181 = 0

using Newton-Raphson:

x \approx 4.34256 \dots

Apply long division:

\frac{90 x ^{3} - 1350 x ^{2} + 6740 x - 11181}{x - 4.34256 \dots} = 90 x^{2} - 959.16933 \dots x + 2574.74675 \dots

90 x^{2} - 959.16933 \dots x + 2574.74675 \dots \approx 0

Find one solution for

90 x^{2} - 959.16933 \dots x + 2574.74675 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 4.34256 \dots

7 x^{3} + 3 x^{2} - 29 x + 11 = 0

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

x^{3} - 12 x^{2} - 56 x + 552 = 0

11 x^{10} = 15 x - 9

x^{6} - 8 x^{3} + 1 = 0

What are the solutions to the equation x=6.9+9(x-5)^3 ?
The solutions to the equation x=6.9+9(x-5)^3 are x\approx 4.34256…
Find the zeros of x=6.9+9(x-5)^3
The zeros of x=6.9+9(x-5)^3 are x\approx 4.34256…