Solve the equation by making an appropriate substitution.
-$$x - 8 \sqrt { x } - 128 = 0$$
A) $\{ 256 \}$
B) $\{ 128 \}$
C) $\{ 512 \}$
D) $\{ 192 \}$

Question

Quizplus · Accepted Answer

Substitute $u = \sqrt{x}$, then $x = u^2$. The equation becomes $u^2 - 8u - 128 = 0$. Factoring or using the quadratic formula gives $u = 16$ or $u = -8$. Since $u = \sqrt{x}$ must be positive, $u = 16$. Thus, $x = u^2 = 256$.

Solve the Equation by Making an Appropriate Substitution x−8x−128=0x - 8 \sqrt { x } - 128 = 0x−8x​−128=0

Solve the Equation by Making an Appropriate Substitution $x - 8 \sqrt { x } - 128 = 0$