solve by factoring $-3(t-1)^2+12=0$.

$t=$

and

$t=$

Question

solve by factoring $-3(t-1)^2+12=0$.

$t=$

and

$t=$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Quadratic Equations", "Quadratic Factoring" ], "new_concepts": [], "current_concepts": [ "Quadratic Equations", "Quadratic Factoring", "Difference of Squares" ] } ## Isolate the squared term $$ \begin{aligned} -3(t-1)^2 + 12 &= 0 \ -3(t-1)^2 &= -12 \ (t-1)^2 &= 4 \end{aligned} $$ ## Factor using difference of squares $$ \begin{aligned} (t-1)^2 - 4 &= 0 \ ((t-1) - 2)((t-1) + 2) &= 0 \ (t-3)(t+1) &= 0 \end{aligned} $$ ## Solve for t $$ \begin{aligned} t - 3 = 0 &\implies t = 3 \ t + 1 = 0 &\implies t = -1 \end{aligned} $$ $t = 3$ and $t = -1$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Quadratic Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Isolate the squared term

Factor using difference of squares

Solve for t

Answer: