solve by factoring $-4(e-1)^2+16=0$.

$e =$

and

Question

solve by factoring $-4(e-1)^2+16=0$.

$e =$

and

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Quadratic Equations", "Polynomial Factoring" ], "new_concepts": [], "current_concepts": [ "Quadratic Equations", "Polynomial Factoring", "Solving for Variables" ] } ## Divide by the common factor $$ \begin{aligned} -4(e-1)^2 + 16 &= 0 \ (e-1)^2 - 4 &= 0 \end{aligned} $$ ## Factor using difference of squares $$ \begin{aligned} ((e-1) - 2)((e-1) + 2) &= 0 \ (e - 3)(e + 1) &= 0 \end{aligned} $$ ## Solve for the variable $$ \begin{aligned} e - 3 = 0 &\implies e = 3 \ e + 1 = 0 &\implies e = -1 \end{aligned} $$ Solve by factoring $-4(e-1)^2+16=0$. $e =$ $3$ and $-1$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Quadratic Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Divide by the common factor

Factor using difference of squares

Solve for the variable

Answer: