Question

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$2 \sqrt{x} - 14 = \frac{288}{ \sqrt{x} }$
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Answer 1

Answer:

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Answer 2

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Here's the solution ~

• $\sf 2\sqrt{x} - 14 = \dfrac{288}{ \sqrt{x} }$

• $\sf \sqrt{x} (2 \sqrt{x} - 14) = 288$

• $\sf 2x - 14 \sqrt{x} - 288 = 0$

• $\sf2x - 32 \sqrt{x} + 18 \sqrt{x} - 288 = 0$

• $\sf2 \sqrt{x} ( \sqrt{x} - 16) + 18( \sqrt{x } - 16 ) = 0$

• $\sf(2 \sqrt{x} + 18) ( \sqrt{x} - 16) = 0$

There are two cases now ~

Case #1

• $\sf2 \sqrt{x} + 18 = 0$

• $\sf2 \sqrt{x} = - 18$

• $\sf \sqrt{x} = - 18 \div 2$

• $\sf \sqrt{x} = - 9$

• $\sf x = ( - 9) {}^{2}$

• $\sf{x = 81}$

Case #2

• $\sf \sqrt{x} - 16 = 0$

• $\sf \sqrt{x} = 16$

• $\sf x = (16) {}^{2}$

• $\sf{x = 256}$