What is the answer to -9x^{1/2}+x^{3/2}=16 ?

The answer to -9x^{1/2}+x^{3/2}=16 is x\approx 13.37495…

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-9x^{1/2}+x^{3/2}=16

- 9 x^{\frac{1}{2}} + x^{\frac{3}{2}} = 16

x \approx 13.37495 \dots

Solution steps

- 9 x^{\frac{1}{2}} + x^{\frac{3}{2}} = 16

Factor

- 9 x^{\frac{1}{2}} + x^{\frac{3}{2}} : x^{\frac{1}{2}} (- 9 + x)

x^{\frac{1}{2}} (- 9 + x) = 16

Square both sides:

81 x - 18 x^{2} + x^{3} = 256

81 x - 18 x^{2} + x^{3} = 256

Solve

81 x - 18 x^{2} + x^{3} = 256 : x \approx 13.37495 \dots

x \approx 13.37495 \dots

Verify Solutions:

x \approx 13.37495 \dots

True

The solution is

x \approx 13.37495 \dots

f (x) = x^{2} + 2 x + 2

f (x) = (x - 7)^{\frac{1}{3}}

f (x) = - x^{2} - 6 x + 1

y = \frac{x}{x ^{3} - x + 5}

f (x) = \frac{- 4 x + 4}{x - 5}

What is the answer to -9x^{1/2}+x^{3/2}=16 ?
The answer to -9x^{1/2}+x^{3/2}=16 is x\approx 13.37495…
Solve for x: -9x^{1/2}+x^{3/2}=16
The solution is x\approx 13.37495…