What is the answer to x-2=(10)/(sqrt(x-2))-3 ?

The answer to x-2=(10)/(sqrt(x-2))-3 is x\approx 4.88621…

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x-2=(10)/(sqrt(x-2))-3

x - 2 = \frac{10}{x - 2} - 3

x \approx 4.88621 \dots

Solution steps

x - 2 = \frac{10}{x - 2} - 3

Multiply both sides by

x - 2

x x - 2 - 2 x - 2 = \frac{10}{x - 2} x - 2 - 3 x - 2

Simplify

x x - 2 - 2 x - 2 = 10 - 3 x - 2

Factor

x x - 2 - 2 x - 2 : (x - 2) x - 2

(x - 2) x - 2 = 10 - 3 x - 2

Divide both sides by

x - 2

x - 2 = \frac{10 - 3 x - 2}{x - 2}

Multiply both sides by

x - 2

x - 2 (x - 2) = 10 - 3 x - 2

Move

3 x - 2

to the left side

x x - 2 + x - 2 = 10

Factor

x x - 2 + x - 2 : x - 2 (x + 1)

x - 2 (x + 1) = 10

Divide both sides by

x + 1

x - 2 = \frac{10}{x + 1}

Square both sides:

x - 2 = \frac{100}{x ^{2} + 2 x + 1}

x - 2 = \frac{100}{x ^{2} + 2 x + 1}

Solve

x - 2 = \frac{100}{x ^{2} + 2 x + 1} : x \approx 4.88621 \dots

x \approx 4.88621 \dots

Verify Solutions:

x \approx 4.88621 \dots

True

The solution is

x \approx 4.88621 \dots

- 7 = 8 - 3^{5} x^{3}

x^{2} - 3 x + 2 = x - 1

3 x^{\frac{5}{2}} - 28 = 68

x + 3 = x + 11

x - 7 - 2 x = - 1

What is the answer to x-2=(10)/(sqrt(x-2))-3 ?
The answer to x-2=(10)/(sqrt(x-2))-3 is x\approx 4.88621…
Solve for x: x-2=(10)/(sqrt(x-2))-3
The solution is x\approx 4.88621…