Solve Equations That Are Quadratic in Form
Solve the equation by making an appropriate substitution.
-$$x - 2 x ^ { 1 / 2 } - 8 = 0$$
A) $\{ 16 \}$
B) $\{ 8 \}$
C) $\{ 32 \}$
D) $\{ 12 \}$

Question

Quizplus · Accepted Answer

This equation can be solved by making the substitution $u = x^{1/2}$, which transforms the equation into a quadratic form. Substituting gives $u^2 - 2u - 8 = 0$. Factoring or using the quadratic formula yields $u = 4$ or $u = -2$. Since $u = x^{1/2}$, and a square root cannot be negative, we discard $u = -2$. Thus, $x^{1/2} = 4$, and squaring both sides gives $x = 16$.

Solve Equations That Are Quadratic in Form Solve the Equation x−2x1/2−8=0x - 2 x ^ { 1 / 2 } - 8 = 0x−2x1/2−8=0

Solve Equations That Are Quadratic in Form
Solve the Equation $x - 2 x ^ { 1 / 2 } - 8 = 0$