What are the solutions to the equation (8x^7)+(8x^4)=8x(x) ?

The solutions to the equation (8x^7)+(8x^4)=8x(x) are x=0,x\approx 0.80873…

Find the zeros of (8x^7)+(8x^4)=8x(x)

The zeros of (8x^7)+(8x^4)=8x(x) are x=0,x\approx 0.80873…

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(8 x^{7}) + (8 x^{4}) = 8 x (x)

x = 0, x \approx 0.80873 \dots

Solution steps

(8 x^{7}) + (8 x^{4}) = 8 x (x)

Expand

8 x (x) : 8 x^{2}

8 x^{7} + 8 x^{4} = 8 x^{2}

Move

8 x^{2}

to the left side

8 x^{7} + 8 x^{4} - 8 x^{2} = 0

Factor

8 x^{7} + 8 x^{4} - 8 x^{2} : 8 x^{2} (x^{5} + x^{2} - 1)

8 x^{2} (x^{5} + x^{2} - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x^{5} + x^{2} - 1 = 0

Solve

x^{5} + x^{2} - 1 = 0 : x \approx 0.80873 \dots

The solutions are

x = 0, x \approx 0.80873 \dots

x^{4} + i x = i x - i + 3

x^{4} + 6 \cdot x^{2} - 60 x + 36 = 0

x^{4} - 6 x^{2} = 27

x (x - 3) (2 x - 1) = 0

j (x) = 3 x^{3}, [1, 1 + h (x)]

What are the solutions to the equation (8x^7)+(8x^4)=8x(x) ?
The solutions to the equation (8x^7)+(8x^4)=8x(x) are x=0,x\approx 0.80873…
Find the zeros of (8x^7)+(8x^4)=8x(x)
The zeros of (8x^7)+(8x^4)=8x(x) are x=0,x\approx 0.80873…