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2sqrtx-14=(288)/(sqrtx)

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

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Simplify radical expressions involving fractions

Full solution

Q.

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

Isolate square root term: Isolate the term with the square root of $x$ on one side. $\newline$ $2\sqrt{x} = \frac{288}{\sqrt{x}} + 14$
Multiply to eliminate denominator: Multiply both sides by $\sqrt{x}$ to get rid of the denominator. $2\sqrt{x} \times \sqrt{x} = \frac{288}{\sqrt{x}} \times \sqrt{x} + 14 \times \sqrt{x}$
Simplify both sides: Simplify both sides. $\newline$ $2x = 288 + 14\sqrt{x}$
Subtract $288$ : Subtract $288$ from both sides. $\newline$ $2x - 288 = 14\sqrt{x}$
Divide by $2$ : Divide both sides by $2$ . $x - 144 = 7\sqrt{x}$
Square to eliminate square root: Square both sides to eliminate the square root. $\newline$ (x - \(144)^ $2$ = ( $7$ \sqrt{x})^ $2$
Expand and simplify: Expand the left side and simplify the right side. $\newline$ $x^2 - 288x + 20736 = 49x$
Combine like terms: Bring all terms to one side to set the equation to zero. $\newline$ $x^2 - 288x - 49x + 20736 = 0$
Factor quadratic equation: Combine like terms. $\newline$ $x^2 - 337x + 20736 = 0$
Set factors equal: Factor the quadratic equation. $\newline$ $(x - 336)(x - 1) = 0$
Solve for x: Set each factor equal to zero and solve for x. $\newline$ $x - 336 = 0$ or $x - 1 = 0$
Solve for x: Set each factor equal to zero and solve for x. $\newline$ $x - 336 = 0$ or $x - 1 = 0$ Solve for x. $\newline$ $x = 336$ or $x = 1$

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