What is the answer to 100=(4x^2)/((2-x)^2) ?

The answer to 100=(4x^2)/((2-x)^2) is x= 5/2 ,x= 5/3

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100=(4x^2)/((2-x)^2)

100 = \frac{4 x ^{2}}{( 2 - x ) ^{2}}

x = \frac{5}{2}, x = \frac{5}{3}

Decimal Notation

x = 2.5, x = 1.66666 \dots

Solution steps

100 = \frac{4 x ^{2}}{( 2 - x ) ^{2}}

Multiply both sides by

(2 - x)^{2}

100 (2 - x)^{2} = 4 x^{2}

Solve

100 (2 - x)^{2} = 4 x^{2} : x = \frac{5}{2}, x = \frac{5}{3}

x = \frac{5}{2}, x = \frac{5}{3}

Verify Solutions

Find undefined (singularity) points:

x = 2

Combine undefined points with solutions:

x = \frac{5}{2}, x = \frac{5}{3}

1 + \frac{1}{x} = \frac{12}{x ^{2}}

\frac{x ^{3} + x + 2}{x ^{2} + 1} = 2

\frac{7}{3} = \frac{42}{y}

- 4 = \frac{x}{1200 - x}

\frac{5 x - 45}{x - 9} = 5

What is the answer to 100=(4x^2)/((2-x)^2) ?
The answer to 100=(4x^2)/((2-x)^2) is x= 5/2 ,x= 5/3
Solve for x: 100=(4x^2)/((2-x)^2)
The solution is x= 5/2 ,x= 5/3