Solve the equation by making an appropriate substitution.
-$$2 x - 7 \sqrt { x } - 72 = 0$$
A) $\{ 64 \}$
B) $\{ 8 \}$
C) $\left\{ \frac { 81 } { 4 } , 64 \right\}$
D) $\left\{ \frac { 9 } { 2 } , 8 \right\}$

Question

Quizplus · Accepted Answer

Let $u = \sqrt{x}$. Then $u^2 = x$ and $2u \frac{du}{dx} = 1$. Substituting, we get$$2u^2 - 7u - 72 = 0$$$$(2u + 8)(u - 9) = 0$$$$u = -4, 9$$$$x = 16, 81$$$$\therefore x = 8, 64$$

Solve the Equation by Making an Appropriate Substitution 2x−7x−72=02 x - 7 \sqrt { x } - 72 = 02x−7x​−72=0

Solve the Equation by Making an Appropriate Substitution $2 x - 7 \sqrt { x } - 72 = 0$