solve the equation.

\144 - p^2 = 0\

\p = \pm ? \

Question

solve the equation.

\144 - p^2 = 0\

\p = \pm  ? \

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Difference of Squares", "Polynomial Factoring" ], "new_concepts": [], "current_concepts": [ "Difference of Squares", "Polynomial Factoring", "Quadratic Zeros" ] } ## Identify the given equation We are given the quadratic equation: $$144 - p^2 = 0$$ Our goal is to solve for $p$ and find the value that fills the blank in $p = \pm [?]$. ## Apply factoring method Using the **Difference of Squares** knowledge point $$ \begin{aligned} &144 - p^2 = 12^2 - p^2\ &(12 - p)(12 + p) = 0 \end{aligned} $$ ## Solve for the variable Using the **Polynomial Factoring** knowledge point $$ \begin{aligned} &12 - p = 0 \implies p = 12\ &12 + p = 0 \implies p = -12\ &p = \pm 12 \end{aligned} $$ Solve the equation. $144 - p^2 = 0$ $p = \pm$ 12 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Difference of Squares" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the given equation

Apply factoring method

Solve for the variable

Answer: