solve the following equation by factoring. separate multiple answers with a comma, if necessary.

\(x + 1)(x + 1) = 16\

Question

solve the following equation by factoring. separate multiple answers with a comma, if necessary.

\(x + 1)(x + 1) = 16\

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": [ "Polynomial Multiplication", "Standard Form of Quadratic Equations", "Factoring Quadratic Equations", "Zero Product Property" ], "new_concepts": [], "current_concepts": [ "Polynomial Multiplication", "Standard Form of Quadratic Equations", "Factoring Quadratic Equations", "Zero Product Property" ] } ## Expand the left side Using the *Polynomial Multiplication* knowledge point $$ (x + 1)(x + 1) = x^2 + 2x + 1 $$ ## Write in standard form Using the *Standard Form of Quadratic Equations* knowledge point $$ \begin{aligned} x^2 + 2x + 1 &= 16 \ x^2 + 2x - 15 &= 0 \end{aligned} $$ ## Factor the quadratic equation Using the *Factoring Quadratic Equations* knowledge point $$ (x + 5)(x - 3) = 0 $$ ## Apply the zero product property Using the *Zero Product Property* knowledge point $$ \begin{aligned} x + 5 = 0 \quad &\Rightarrow \quad x = -5 \ x - 3 = 0 \quad &\Rightarrow \quad x = 3 \end{aligned} $$ Solve the following equation by factoring. Separate multiple answers with a comma, if necessary. $$(x + 1)(x + 1) = 16$$ $x =$ $-5, 3$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Solving Quadratic Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Expand the left side

Write in standard form

Factor the quadratic equation

Apply the zero product property

Answer: