what are the solutions of the equation $(x - 3)^2 + 2(x - 3) - 8 = 0$? use $u$ substitution to solve.

$x = -5$ and $x = 1$
$x = -1$ and $x = 5$
$x = -1$ and $x = -7$
$x = 1$ and $x = 7$

Question

what are the solutions of the equation $(x - 3)^2 + 2(x - 3) - 8 = 0$? use $u$ substitution to solve.

$x = -5$ and $x = 1$
$x = -1$ and $x = 5$
$x = -1$ and $x = -7$
$x = 1$ and $x = 7$

Accepted Answer

{ "quality": "clear", "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" ], "new_concepts": [], "current_concepts": [ "Quadratic Form Equations", "Polynomial Factoring" ] } ## Define the substitution variable Using the *Quadratic Form Equations* knowledge point $$ \text{Let } u = x - 3 $$ ## Rewrite and solve the quadratic equation Using the *Quadratic Form Equations* knowledge point $$ \begin{aligned} &u^2 + 2u - 8 = 0 \ &(u + 4)(u - 2) = 0 \ &u = -4 \quad \text{or} \quad u = 2 \end{aligned} $$ ## Substitute back to solve for x Using the *Quadratic Form Equations* knowledge point $$ \begin{aligned} &x - 3 = -4 \implies x = -1 \ &x - 3 = 2 \implies x = 5 \end{aligned} $$

(A) $x = -5$ and $x = 1$

(B) $x = -1$ and $x = 5$

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

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

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

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QUESTION IMAGE

Question

Explanation:

Define the substitution variable

Rewrite and solve the quadratic equation

Substitute back to solve for x

Answer: