solve the equation by factoring. enter the smallest solution first.

\21x^2 - 6 = 15x\

\x = -\frac{?}{ }, \

Question

solve the equation by factoring. enter the smallest solution first.

\21x^2 - 6 = 15x\

\x = -\frac{?}{ },  \

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": [ "Solving Quadratic Equations", "Greatest Common Factor", "Polynomial Factoring" ], "new_concepts": [], "current_concepts": [ "Solving Quadratic Equations", "Greatest Common Factor", "Polynomial Factoring" ] } ## Rearrange the quadratic equation Using the **Solving Quadratic Equations** knowledge point $$ \begin{aligned} 21x^2 - 6 &= 15x \ 21x^2 - 15x - 6 &= 0 \end{aligned} $$ ## Factor out the greatest common factor Using the **Greatest Common Factor** knowledge point $$ \begin{aligned} 3(7x^2 - 5x - 2) &= 0 \ 7x^2 - 5x - 2 &= 0 \end{aligned} $$ ## Factor the trinomial Using the **Polynomial Factoring** knowledge point $$ \begin{aligned} 7x^2 - 7x + 2x - 2 &= 0 \ 7x(x - 1) + 2(x - 1) &= 0 \ (7x + 2)(x - 1) &= 0 \end{aligned} $$ ## Solve for x Using the **Solving Quadratic Equations** knowledge point $$ \begin{aligned} 7x + 2 = 0 &\implies x = -\frac{2}{7} \ x - 1 = 0 &\implies x = 1 \end{aligned} $$ ## Identify the smallest solution Comparing the two solutions: $$ -\frac{2}{7} < 1 $$ The smallest solution is $-\frac{2}{7}$ and the larger solution is $1$. Solve the equation by factoring. Enter the smallest solution first. $21x^2 - 6 = 15x$ $x =$ $-\frac{2}{7}$, $1$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Solving Quadratic Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Rearrange the quadratic equation

Factor out the greatest common factor

Factor the trinomial

Solve for x

Identify the smallest solution

Answer: