What are the solutions to the equation 7x^9=(7x^{10})-(7x) ?

The solutions to the equation 7x^9=(7x^{10})-(7x) are x=0,x\approx 1.21314…

Find the zeros of 7x^9=(7x^{10})-(7x)

The zeros of 7x^9=(7x^{10})-(7x) are x=0,x\approx 1.21314…

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7 x^{9} = (7 x^{10}) - (7 x)

x = 0, x \approx 1.21314 \dots

Solution steps

7 x^{9} = (7 x^{10}) - (7 x)

Refine

7 x^{9} = 7 x^{10} - 7 x

Switch sides

7 x^{10} - 7 x = 7 x^{9}

Move

7 x^{9}

to the left side

7 x^{10} - 7 x - 7 x^{9} = 0

Factor

7 x^{10} - 7 x - 7 x^{9} : 7 x (x^{9} - x^{8} - 1)

7 x (x^{9} - x^{8} - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x^{9} - x^{8} - 1 = 0

Solve

x^{9} - x^{8} - 1 = 0 : x \approx 1.21314 \dots

The solutions are

x = 0, x \approx 1.21314 \dots

x, 27 x^{4} + 60 x^{2} = 32

8 x^{3} = 0

0 = x^{4} - 18 x^{2} + 32

x (x - 5)^{3} - 14 (x - 5)^{2} = 0

4 x (x - 3)^{2} (2 x - 5) = 0

What are the solutions to the equation 7x^9=(7x^{10})-(7x) ?
The solutions to the equation 7x^9=(7x^{10})-(7x) are x=0,x\approx 1.21314…
Find the zeros of 7x^9=(7x^{10})-(7x)
The zeros of 7x^9=(7x^{10})-(7x) are x=0,x\approx 1.21314…