what are the solutions of (-x^2 + 4x = x - 4)?

-5 and 0
-5 and -1
-1 and 4
0 and 4

Question

what are the solutions of (-x^2 + 4x = x - 4)?

-5 and 0
-5 and -1
-1 and 4
0 and 4

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Solving Quadratic Equations", "Graphical Intersection of Systems" ], "new_concepts": [], "current_concepts": [ "Solving Quadratic Equations", "Graphical Intersection of Systems" ] } ## Set up the quadratic equation $$ -x^2 + 4x = x - 4 $$ ## Rearrange into standard form $$ \begin{aligned} -x^2 + 3x + 4 &= 0 \ x^2 - 3x - 4 &= 0 \end{aligned} $$ ## Factor and solve for x $$ \begin{aligned} (x - 4)(x + 1) &= 0 \ x = 4 \quad &\text{or} \quad x = -1 \end{aligned} $$

-5 and 0

-5 and -1

-1 and 4

0 and 4

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

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QUESTION IMAGE

Question

Explanation:

Set up the quadratic equation

Rearrange into standard form

Factor and solve for x

Answer: