What is the answer to (x^{3/2})/(x-6)=x-8 ?

The answer to (x^{3/2})/(x-6)=x-8 is x=4,x\approx 14.49616…

Solve for x: (x^{3/2})/(x-6)=x-8

The solution is x=4,x\approx 14.49616…

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\frac{x ^{\frac{3}{2}}}{x - 6} = x - 8

x = 4, x \approx 14.49616 \dots

Solution steps

\frac{x ^{\frac{3}{2}}}{x - 6} = x - 8

Multiply both sides by

x - 6

\frac{x ^{\frac{3}{2}}}{x - 6} (x - 6) = x (x - 6) - 8 (x - 6)

Simplify

x^{\frac{3}{2}} = x (x - 6) - 8 (x - 6)

Expand

x (x - 6) - 8 (x - 6) : x^{2} - 14 x + 48

x^{\frac{3}{2}} = x^{2} - 14 x + 48

Take both sides of the equation to the power of

2 : x^{3} = x^{4} - 28 x^{3} + 292 x^{2} - 1344 x + 2304

x^{3} = x^{4} - 28 x^{3} + 292 x^{2} - 1344 x + 2304

Solve

x^{3} = x^{4} - 28 x^{3} + 292 x^{2} - 1344 x + 2304 : x = 4, x \approx 14.49616 \dots

x = 4, x \approx 14.49616 \dots

Verify Solutions:

x = 4

True

, x \approx 14.49616 \dots

True

The solutions are

x = 4, x \approx 14.49616 \dots

x^{\frac{3}{2}} + 4 = 0

x - 1 + 5 = 9

x + 1 = 3 x - 1

3 x - 5 + x - 1 = 2

8 x - 17 = 1

What is the answer to (x^{3/2})/(x-6)=x-8 ?
The answer to (x^{3/2})/(x-6)=x-8 is x=4,x\approx 14.49616…
Solve for x: (x^{3/2})/(x-6)=x-8
The solution is x=4,x\approx 14.49616…