select the correct answer.

what are the solutions of this quadratic equation?

(x^2 + 4 = 8x + 5)

(x = 8 pm sqrt{34})
(x = 8 pm 2sqrt{17})
(x = 4 pm sqrt{7})
(x = 4 pm sqrt{17})

Question

select the correct answer.

what are the solutions of this quadratic equation?

(x^2 + 4 = 8x + 5)

(x = 8 pm sqrt{34})
(x = 8 pm 2sqrt{17})
(x = 4 pm sqrt{7})
(x = 4 pm sqrt{17})

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Quadratic Formula Application" ], "new_concepts": [], "current_concepts": [ "Quadratic Equations", "Quadratic Formula Application" ] } ## Rearrange the equation into standard form $$ \begin{aligned} x^2 + 4 &= 8x + 5 \ x^2 - 8x - 1 &= 0 \end{aligned} $$ ## Apply the quadratic formula $$ \begin{aligned} x &= \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \ x &= \frac{-(-8) \pm \sqrt{(-8)^2 - 4(1)(-1)}}{2(1)} \ x &= \frac{8 \pm \sqrt{64 + 4}}{2} \ x &= \frac{8 \pm \sqrt{68}}{2} \end{aligned} $$ ## Simplify the radical expression $$ \begin{aligned} x &= \frac{8 \pm \sqrt{4 \times 17}}{2} \ x &= \frac{8 \pm 2\sqrt{17}}{2} \ x &= 4 \pm \sqrt{17} \end{aligned} $$

(A) $x = 8 \pm \sqrt{34}$

(B) $x = 8 \pm 2\sqrt{17}$

(C) $x = 4 \pm \sqrt{7}$

(D) $x = 4 \pm \sqrt{17}$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Quadratic Formula Application" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Rearrange the equation into standard form

Apply the quadratic formula

Simplify the radical expression

Answer: