What is the answer to 2sqrt(x)-14=(288)/((sqrt(x))) ?

The answer to 2sqrt(x)-14=(288)/((sqrt(x))) is x=256

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2sqrt(x)-14=(288)/((sqrt(x)))

2 x - 14 = \frac{288}{( x )}

x = 256

Solution steps

2 x - 14 = \frac{288}{( x )}

Multiply both sides by

x

2 x x - 14 x = \frac{288}{x} x

Simplify

2 (x)^{2} - 14 x = 288

Move

288

to the left side

2 (x)^{2} - 14 x - 288 = 0

Factor

2 (x)^{2} - 14 x - 288 : 2 (x + 9) (x - 16)

2 (x + 9) (x - 16) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x + 9 = 0 or x - 16 = 0

Solve

x + 9 = 0 :

No Solution for

x \in R

Solve

x - 16 = 0 : x = 256

x = 256

Verify Solutions:

x = 256

True

The solution is

x = 256

3 x^{2} - 2 6 x + 2 = 0

x^{\frac{2}{5}} - 3 x^{\frac{1}{5}} + 2 = 0

a, c = a^{2} + b^{2}

x^{2} - 2 3 x + 3 = 0

x + 2 = 3

What is the answer to 2sqrt(x)-14=(288)/((sqrt(x))) ?
The answer to 2sqrt(x)-14=(288)/((sqrt(x))) is x=256
Solve for x: 2sqrt(x)-14=(288)/((sqrt(x)))
The solution is x=256