Question was provided via image upload.

Question

Accepted Answer

{ "quality": "blurry", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Quadratic Form Equations", "Polynomial Factoring" ], "new_concepts": [], "current_concepts": [ "Quadratic Form Equations", "Polynomial Factoring", "u-Substitution" ] } ## Define the substitution variable Using the *Quadratic Form Equations* knowledge point $$ \begin{aligned} &\text{Let } u = x - 2\ &\text{The equation } (x - 2)^2 - 2(x - 2) - 15 = 0 \text{ becomes:}\ &u^2 - 2u - 15 = 0 \end{aligned} $$ ## Factor the quadratic equation Using the *Polynomial Factoring* knowledge point $$ \begin{aligned} &(u - 5)(u + 3) = 0\ &u = 5 \quad \text{or} \quad u = -3 \end{aligned} $$ ## Solve for the original variable Substitute $u = x - 2$ back into the equations: $$ \begin{aligned} &x - 2 = 5 \implies x = 7\ &x - 2 = -3 \implies x = -1 \end{aligned} $$ Thus, the solutions are $x = -1$ and $x = 7$.

(A) $x = -7$ and $x = 1$

(B) $x = -5$ and $x = 3$

(C) $x = -3$ and $x = 5$

(D) $x = -1$ and $x = 7$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Quadratic Form Equations" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Define the substitution variable

Factor the quadratic equation

Solve for the original variable

Answer: