select the correct answer.

what is the solution to the equation?

$\sqrt{-2x - 5} - 4 = x$

-7 and -3
3 and 7
-3
7

Question

select the correct answer.

what is the solution to the equation?

$\sqrt{-2x - 5} - 4 = x$

-7 and -3
3 and 7
-3
7

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Radical Equations", "Extraneous Solutions" ], "new_concepts": [], "current_concepts": [ "Radical Equations", "Extraneous Solutions" ] } ## Isolate the radical and square both sides $$ \begin{aligned} \sqrt{-2x - 5} - 4 &= x \ \sqrt{-2x - 5} &= x + 4 \ -2x - 5 &= (x + 4)^2 \ -2x - 5 &= x^2 + 8x + 16 \end{aligned} $$ ## Solve the quadratic equation $$ \begin{aligned} x^2 + 10x + 21 &= 0 \ (x + 7)(x + 3) &= 0 \ x = -7 \quad &\text{or} \quad x = -3 \end{aligned} $$ ## Check for extraneous solutions $$ \begin{aligned} \text{For } x = -7: \quad \sqrt{-2(-7) - 5} - 4 &= \sqrt{9} - 4 = 3 - 4 = -1 eq -7 \quad (\text{Extraneous}) \ \text{For } x = -3: \quad \sqrt{-2(-3) - 5} - 4 &= \sqrt{1} - 4 = 1 - 4 = -3 = -3 \quad (\text{Valid}) \end{aligned} $$

-7 and -3

3 and 7

-3

7

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Radical Equations" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Isolate the radical and square both sides

Solve the quadratic equation

Check for extraneous solutions

Answer: