solve for $x$ in the equation $2x^2 - 5x + 1 = 3$.

$x = \frac{5}{2} \pm \frac{\sqrt{29}}{2}$

$x = \frac{5}{2} \pm \frac{\sqrt{41}}{4}$

$x = \frac{5}{4} \pm \frac{\sqrt{29}}{2}$

$x = \frac{5}{4} \pm \frac{\sqrt{41}}{4}$

Question

solve for $x$ in the equation $2x^2 - 5x + 1 = 3$.

$x = \frac{5}{2} \pm \frac{\sqrt{29}}{2}$

$x = \frac{5}{2} \pm \frac{\sqrt{41}}{4}$

$x = \frac{5}{4} \pm \frac{\sqrt{29}}{2}$

$x = \frac{5}{4} \pm \frac{\sqrt{41}}{4}$

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 Formula" ] } ## Rearrange the quadratic equation into standard form $$ \begin{aligned} 2x^2 - 5x + 1 &= 3 \ 2x^2 - 5x - 2 &= 0 \end{aligned} $$ ## Apply the quadratic formula $$ \begin{aligned} x &= \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \ x &= \frac{-(-5) \pm \sqrt{(-5)^2 - 4(2)(-2)}}{2(2)} \ x &= \frac{5 \pm \sqrt{25 + 16}}{4} \ x &= \frac{5 \pm \sqrt{41}}{4} \end{aligned} $$ ## Express the solution in the matching format $$ x = \frac{5}{4} \pm \frac{\sqrt{41}}{4} $$

(A) $x = \frac{5}{2} \pm \frac{\sqrt{29}}{2}$

(B) $x = \frac{5}{2} \pm \frac{\sqrt{41}}{4}$

(C) $x = \frac{5}{4} \pm \frac{\sqrt{29}}{2}$

(D) $x = \frac{5}{4} \pm \frac{\sqrt{41}}{4}$

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

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Rearrange the quadratic equation into standard form

Apply the quadratic formula

Express the solution in the matching format

Answer: