What is the answer to (8+x)^{-3}=64 ?

The answer to (8+x)^{-3}=64 is x=-31/4 ,x=-65/8+i(sqrt(3))/8 ,x=-65/8-i(sqrt(3))/8

Solve for x: (8+x)^{-3}=64

The solution is x=-31/4 ,x=-65/8+i(sqrt(3))/8 ,x=-65/8-i(sqrt(3))/8

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(8 + x)^{- 3} = 64

x = - \frac{31}{4}, x = - \frac{65}{8} + i \frac{3}{8}, x = - \frac{65}{8} - i \frac{3}{8}

Solution steps

(8 + x)^{- 3} = 64

Refine

\frac{1}{( 8 + x ) ^{3}} = 64

Multiply both sides by

(8 + x)^{3}

1 = 64 (8 + x)^{3}

Solve

1 = 64 (8 + x)^{3} : x = - \frac{31}{4}, x = - \frac{65}{8} + i \frac{3}{8}, x = - \frac{65}{8} - i \frac{3}{8}

x = - \frac{31}{4}, x = - \frac{65}{8} + i \frac{3}{8}, x = - \frac{65}{8} - i \frac{3}{8}

Verify Solutions

Find undefined (singularity) points:

x = - 8

Combine undefined points with solutions:

x = - \frac{31}{4}, x = - \frac{65}{8} + i \frac{3}{8}, x = - \frac{65}{8} - i \frac{3}{8}

1 - \frac{8}{x ^{3}} = 0

x^{- 2} + 2 x^{- 1} - 8 = 0

2 - \frac{1}{7 x} = \frac{10}{7}

\frac{x}{2 x + 7} = \frac{x - 5}{x - 1}

\frac{x - 4}{3 x + 2} = \frac{3}{7}

What is the answer to (8+x)^{-3}=64 ?
The answer to (8+x)^{-3}=64 is x=-31/4 ,x=-65/8+i(sqrt(3))/8 ,x=-65/8-i(sqrt(3))/8
Solve for x: (8+x)^{-3}=64
The solution is x=-31/4 ,x=-65/8+i(sqrt(3))/8 ,x=-65/8-i(sqrt(3))/8