\2x^2 - 3x - 2 = x + 4\

the equation is represented by the system shown here.

check all of the solutions to this equation.
-1
3
7
(-1, 3)
(3, 7)

Question

\2x^2 - 3x - 2 = x + 4\

the equation is represented by the system shown here.

check all of the solutions to this equation.
-1
3
7
(-1, 3)
(3, 7)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Solving Quadratic Equations" ], "new_concepts": [], "current_concepts": [ "Solving Quadratic Equations", "Quadratic Graphs" ] } ## Write the equation in standard form $$ \begin{aligned} 2x^2 - 3x - 2 &= x + 4 \ 2x^2 - 4x - 6 &= 0 \end{aligned} $$ ## Solve the quadratic equation by factoring $$ \begin{aligned} 2(x^2 - 2x - 3) &= 0 \ 2(x - 3)(x + 1) &= 0 \ x = 3 \quad &\text{or} \quad x = -1 \end{aligned} $$ ## Identify the solutions to the single-variable equation $$ \begin{aligned} &\text{The original equation is in terms of } x \text{ only.} \ &\text{Therefore, the solutions are the } x\text{-values of the intersection points:} \ &x = -1 \quad \text{and} \quad x = 3 \end{aligned} $$

-1

3

7

(-1, 3)

(3, 7)

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

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Write the equation in standard form

Solve the quadratic equation by factoring

Identify the solutions to the single-variable equation

Answer: