Solve Radical Equations
-$$\sqrt { 6 x + 16 } = x$$
A) $\{ 8 \}$
B) $\{ - 2,8 \}$
C) $\left\{ - \frac { 16 } { 5 } \right\}$
D) $\varnothing$

Question

Quizplus · Accepted Answer

To solve the equation $\sqrt{6x + 16} = x$, we first square both sides to eliminate the square root, resulting in $6x + 16 = x^2$. Rearranging the equation to set it to 0 gives $x^2 - 6x - 16 = 0$. Factoring or using the quadratic formula, we find that the solutions are $x = -2$ and $x = 8$. However, when we substitute $x = -2$ back into the original equation, it does not satisfy the equation because the square root of a number cannot be negative. Therefore, the only solution that works in the original equation is $x = 8$.

Solve Radical Equations - 6x+16=x\sqrt { 6 x + 16 } = x6x+16​=x

Solve Radical Equations
- $\sqrt { 6 x + 16 } = x$