What is the answer to 100=(8x)/(1+sqrt(x)) ?

The answer to 100=(8x)/(1+sqrt(x)) is x=(11600+sqrt(132000000))/(128)

Solve for x: 100=(8x)/(1+sqrt(x))

The solution is x=(11600+sqrt(132000000))/(128)

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100 = \frac{8 x}{1 + x}

x = \frac{11600 + 132000000}{128}

Decimal Notation

x = 180.38379 \dots

Solution steps

100 = \frac{8 x}{1 + x}

Multiply both sides by

1 + x

100 (1 + x) = \frac{8 x}{1 + x} (1 + x)

Simplify

100 (1 + x) = 8 x

Expand

100 (1 + x) : 100 + 100 x

100 + 100 x = 8 x

Remove square roots

10000 x = 64 x^{2} - 1600 x + 10000

Solve

10000 x = 64 x^{2} - 1600 x + 10000 : x = \frac{11600 + 132000000}{128}, x = \frac{11600 - 132000000}{128}

x = \frac{11600 + 132000000}{128}, x = \frac{11600 - 132000000}{128}

Verify Solutions:

x = \frac{11600 + 132000000}{128}

True

, x = \frac{11600 - 132000000}{128}

False

The solution is

x = \frac{11600 + 132000000}{128}

- x + 12 = x

y + 6 = 2 y^{2} + 72

x, x - y = 1

x = 2 x - 1

What is the answer to 100=(8x)/(1+sqrt(x)) ?
The answer to 100=(8x)/(1+sqrt(x)) is x=(11600+sqrt(132000000))/(128)
Solve for x: 100=(8x)/(1+sqrt(x))
The solution is x=(11600+sqrt(132000000))/(128)