find the real solution of the following radical equation.

(c - \sqrt{14 - 2c} = 7)

(c = ?)

Question

find the real solution of the following radical equation.

(c - \sqrt{14 - 2c} = 7)

(c = ?)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Radical Equations", "Solving Radical Equations", "Extraneous Solutions" ], "new_concepts": [], "current_concepts": [ "Radical Equations", "Solving Radical Equations", "Extraneous Solutions" ] } ## Isolate the radical term $$ \begin{aligned} c - 7 = \sqrt{14 - 2c} \end{aligned} $$ ## Square both sides and solve the quadratic equation $$ \begin{aligned} (c - 7)^2 &= 14 - 2c \ c^2 - 14c + 49 &= 14 - 2c \ c^2 - 12c + 35 &= 0 \ (c - 5)(c - 7) &= 0 \ c = 5 \quad &\text{or} \quad c = 7 \end{aligned} $$ ## Check for extraneous solutions $$ \begin{aligned} \text{For } c = 5: \quad 5 - \sqrt{14 - 2(5)} &= 5 - \sqrt{4} = 3 eq 7 \quad (\text{Extraneous}) \ \text{For } c = 7: \quad 7 - \sqrt{14 - 2(7)} &= 7 - \sqrt{0} = 7 \quad (\text{Valid}) \end{aligned} $$ Find the real solution of the following radical equation. $c - \sqrt{14 - 2c} = 7$ $c =$ 7 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Solving Radical Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Isolate the radical term

Square both sides and solve the quadratic equation

Check for extraneous solutions

Answer: