What is the answer to 64=(x^2)/((1-x)^2) ?

The answer to 64=(x^2)/((1-x)^2) is x= 8/7 ,x= 8/9

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64=(x^2)/((1-x)^2)

64 = \frac{x ^{2}}{( 1 - x ) ^{2}}

x = \frac{8}{7}, x = \frac{8}{9}

Decimal Notation

x = 1.14285 \dots, x = 0.88888 \dots

Solution steps

64 = \frac{x ^{2}}{( 1 - x ) ^{2}}

Multiply both sides by

(1 - x)^{2}

64 (1 - x)^{2} = x^{2}

Solve

64 (1 - x)^{2} = x^{2} : x = \frac{8}{7}, x = \frac{8}{9}

x = \frac{8}{7}, x = \frac{8}{9}

Verify Solutions

Find undefined (singularity) points:

x = 1

Combine undefined points with solutions:

x = \frac{8}{7}, x = \frac{8}{9}

\frac{x}{x ^{2} + 1} = 0

\frac{5}{x - 9} = \frac{8}{x + 5}

\frac{4}{3 x + 3} = \frac{7}{x + 5}

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

\frac{4}{x} = \frac{10}{30}

What is the answer to 64=(x^2)/((1-x)^2) ?
The answer to 64=(x^2)/((1-x)^2) is x= 8/7 ,x= 8/9
Solve for x: 64=(x^2)/((1-x)^2)
The solution is x= 8/7 ,x= 8/9