consider the following quadratic equation:
\x^2 = 49\
step 1 of 2: using the standard form $ax^2 + bx + c = 0$ of the given quadratic equation, factor the left hand side of the equation into two linear factors.

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Standard Form of Quadratic Equations", "Difference of Squares" ], "new_concepts": [], "current_concepts": [ "Standard Form of Quadratic Equations", "Difference of Squares", "Factoring Quadratic Equations" ] } ## Write the equation in standard form Using the *Standard Form of Quadratic Equations* knowledge point $$ \begin{aligned} x^2 &= 49 \ x^2 - 49 &= 0 \end{aligned} $$ ## Factor the left-hand side Using the *Difference of Squares* knowledge point $$ \begin{aligned} x^2 - 7^2 &= 0 \ (x - 7)(x + 7) &= 0 \end{aligned} $$ Using the standard form $ax^2 + bx + c = 0$ of the given quadratic equation, factor the left hand side of the equation into two linear factors: $(x - 7)(x + 7)$ $= 0$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Factoring Quadratic Equations" ] }

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Explanation:

Write the equation in standard form

Factor the left-hand side

Answer: