Solve the radical equation, and check all proposed solutions.
-$$\sqrt { 6 x + 55 } = x$$
A) $\{ - 11 \}$
B) $\varnothing$
C) $\{ 11 \}$
D) $\{ - 5,11 \}$

Question

Quizplus · Accepted Answer

Squaring both sides of the equation $\sqrt{6x + 55} = x$ gives $6x + 55 = x^2$. Rearranging to $x^2 - 6x - 55 = 0$, we can solve this quadratic equation to find $x$. Factoring or using the quadratic formula yields $x = -5$ or $x = 11$. However, when we substitute $x = -5$ back into the original equation, it does not satisfy the equation, leaving $x = 11$ as the only solution.

Solve the Radical Equation, and Check All Proposed Solutions 6x+55=x\sqrt { 6 x + 55 } = x6x+55​=x

Solve the Radical Equation, and Check All Proposed Solutions $\sqrt { 6 x + 55 } = x$