What are the solutions to the equation (3x+9)^5=32x^5 ?

The solutions to the equation (3x+9)^5=32x^5 are x=-9

Find the zeros of (3x+9)^5=32x^5

The zeros of (3x+9)^5=32x^5 are x=-9

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(3 x + 9)^{5} = 32 x^{5}

x = - 9

Solution steps

(3 x + 9)^{5} = 32 x^{5}

Expand

(3 x + 9)^{5} : 243 x^{5} + 3645 x^{4} + 21870 x^{3} + 65610 x^{2} + 98415 x + 59049

243 x^{5} + 3645 x^{4} + 21870 x^{3} + 65610 x^{2} + 98415 x + 59049 = 32 x^{5}

Move

32 x^{5}

to the left side

211 x^{5} + 3645 x^{4} + 21870 x^{3} + 65610 x^{2} + 98415 x + 59049 = 0

Factor

211 x^{5} + 3645 x^{4} + 21870 x^{3} + 65610 x^{2} + 98415 x + 59049 : (x + 9) (211 x^{4} + 1746 x^{3} + 6156 x^{2} + 10206 x + 6561)

(x + 9) (211 x^{4} + 1746 x^{3} + 6156 x^{2} + 10206 x + 6561) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x + 9 = 0 or 211 x^{4} + 1746 x^{3} + 6156 x^{2} + 10206 x + 6561 = 0

Solve

x + 9 = 0 : x = - 9

Solve

211 x^{4} + 1746 x^{3} + 6156 x^{2} + 10206 x + 6561 = 0 :

No Solution for

x \in R

The solution is

x = - 9

\frac{( x ^{4} - 1 )}{20 + 1} = 5

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

2 x^{2} x^{4} x^{4} = 512

(x - 4)^{3} = (\frac{1}{8})^{- 1}

(x - 2) (x + 3) (x - 5) = 0

What are the solutions to the equation (3x+9)^5=32x^5 ?
The solutions to the equation (3x+9)^5=32x^5 are x=-9
Find the zeros of (3x+9)^5=32x^5
The zeros of (3x+9)^5=32x^5 are x=-9