What are the solutions to the equation (4+3x)*x^5=(4+3x)^5 ?

The solutions to the equation (4+3x)*x^5=(4+3x)^5 are x=-4/3 ,x\approx 86.13315…

Find the zeros of (4+3x)*x^5=(4+3x)^5

The zeros of (4+3x)*x^5=(4+3x)^5 are x=-4/3 ,x\approx 86.13315…

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(4 + 3 x) \cdot x^{5} = (4 + 3 x)^{5}

x = - \frac{4}{3}, x \approx 86.13315 \dots

Decimal Notation

x = - 1.33333 \dots, x = 86.13315 \dots

Solution steps

(4 + 3 x) x^{5} = (4 + 3 x)^{5}

Expand

(4 + 3 x) x^{5} : 4 x^{5} + 3 x^{6}

Expand

(4 + 3 x)^{5} : 1024 + 3840 x + 5760 x^{2} + 4320 x^{3} + 1620 x^{4} + 243 x^{5}

4 x^{5} + 3 x^{6} = 1024 + 3840 x + 5760 x^{2} + 4320 x^{3} + 1620 x^{4} + 243 x^{5}

Subtract

1024 + 3840 x + 5760 x^{2} + 4320 x^{3} + 1620 x^{4} + 243 x^{5}

from both sides

4 x^{5} + 3 x^{6} - (1024 + 3840 x + 5760 x^{2} + 4320 x^{3} + 1620 x^{4} + 243 x^{5}) = 1024 + 3840 x + 5760 x^{2} + 4320 x^{3} + 1620 x^{4} + 243 x^{5} - (1024 + 3840 x + 5760 x^{2} + 4320 x^{3} + 1620 x^{4} + 243 x^{5})

Simplify

3 x^{6} - 239 x^{5} - 1620 x^{4} - 4320 x^{3} - 5760 x^{2} - 3840 x - 1024 = 0

Factor

3 x^{6} - 239 x^{5} - 1620 x^{4} - 4320 x^{3} - 5760 x^{2} - 3840 x - 1024 : (3 x + 4) (x^{5} - 81 x^{4} - 432 x^{3} - 864 x^{2} - 768 x - 256)

(3 x + 4) (x^{5} - 81 x^{4} - 432 x^{3} - 864 x^{2} - 768 x - 256) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

3 x + 4 = 0 or x^{5} - 81 x^{4} - 432 x^{3} - 864 x^{2} - 768 x - 256 = 0

Solve

3 x + 4 = 0 : x = - \frac{4}{3}

Solve

x^{5} - 81 x^{4} - 432 x^{3} - 864 x^{2} - 768 x - 256 = 0 : x \approx 86.13315 \dots

The solutions are

x = - \frac{4}{3}, x \approx 86.13315 \dots

4.328 = 541 (1 + \frac{y}{4})^{15}

x^{4} - 5 x^{3} + x^{2} - 2 x - 15 = 0

x^{3} = 9 x^{2} - 20 x

(3 x - 8) (x + 2) = 2 x^{3}

x^{3} - 6 x - 9 = 0

What are the solutions to the equation (4+3x)*x^5=(4+3x)^5 ?
The solutions to the equation (4+3x)*x^5=(4+3x)^5 are x=-4/3 ,x\approx 86.13315…
Find the zeros of (4+3x)*x^5=(4+3x)^5
The zeros of (4+3x)*x^5=(4+3x)^5 are x=-4/3 ,x\approx 86.13315…