Solve the equation.
-$\sqrt { x ^ { 2 } - 15 } - \sqrt { x + 5 } = 0$

Question

Quizplus · Accepted Answer

To solve the equation $\sqrt { x ^ { 2 } - 15 } - \sqrt { x + 5 } = 0$, we isolate one of the square roots and square both sides to eliminate it. This gives us $x^2 - 15 = x + 5$. Simplifying, we get $x^2 - x - 20 = 0$, which factors to $(x-5)(x+4) = 0$, yielding solutions $x = 5$ and $x = -4$. Both solutions must be checked in the original equation to ensure they do not result from squaring, which can introduce extraneous solutions. Plugging $x = 5$ and $x = -4$ back into the original equation, we find that both satisfy the equation, thus both are valid solutions.

Solve the Equation x2−15−x+5=0\sqrt { x ^ { 2 } - 15 } - \sqrt { x + 5 } = 0x2−15​−x+5​=0

Solve the Equation $\sqrt { x ^ { 2 } - 15 } - \sqrt { x + 5 } = 0$