consider the following quadratic equation:

\4x^2 - 15x + 1 = -8\

step 2 of 2: solve the quadratic equation by factoring. write your answer in reduced fraction form, if necessary.

answer
how to enter your answer (opens in new window)

Question

consider the following quadratic equation:

\4x^2 - 15x + 1 = -8\

step 2 of 2: solve the quadratic equation by factoring. write your answer in reduced fraction form, if necessary.

answer
how to enter your answer (opens in new window)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Solving Quadratic Equations", "Factoring Trinomials", "Zero Product Property" ], "new_concepts": [], "current_concepts": [ "Solving Quadratic Equations", "Factoring Trinomials", "Zero Product Property" ] } ## Write in standard form Using the *Solving Quadratic Equations* knowledge point $$ \begin{aligned} 4x^2 - 15x + 1 &= -8 \ 4x^2 - 15x + 9 &= 0 \end{aligned} $$ ## Factor the quadratic trinomial Using the *Factoring Trinomials* knowledge point $$ \begin{aligned} &ac = 4 \times 9 = 36,\quad b = -15 \ &\text{Factors of } 36 \text{ that sum to } -15: -12 \text{ and } -3 \ &4x^2 - 12x - 3x + 9 = 0 \ &4x(x - 3) - 3(x - 3) = 0 \ &(4x - 3)(x - 3) = 0 \end{aligned} $$ ## Apply the zero product property Using the *Zero Product Property* knowledge point $$ \begin{aligned} 4x - 3 = 0 &\implies x = \frac{3}{4} \ x - 3 = 0 &\implies x = 3 \end{aligned} $$ $x = \frac{3}{4}, 3$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Solving Quadratic Equations" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Write in standard form

Factor the quadratic trinomial

Apply the zero product property

Answer: