solve for $x$ in the equation $x^2 - 12x + 59 = 0$.

$x = -12 \pm \sqrt{85}$
$x = -6 \pm \sqrt{23}i$
$x = 6 \pm \sqrt{23}i$
$x = 12 \pm \sqrt{85}$

Question

solve for $x$ in the equation $x^2 - 12x + 59 = 0$.

$x = -12 \pm \sqrt{85}$
$x = -6 \pm \sqrt{23}i$
$x = 6 \pm \sqrt{23}i$
$x = 12 \pm \sqrt{85}$

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", "Complex Numbers" ], "new_concepts": [], "current_concepts": [ "Solving Quadratic Equations", "Complex Numbers" ] } ## Identify coefficients of the quadratic equation $$ a = 1, \quad b = -12, \quad c = 59 $$ ## Apply the quadratic formula $$ \begin{aligned} x &= \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \ x &= \frac{-(-12) \pm \sqrt{(-12)^2 - 4(1)(59)}}{2(1)} \ x &= \frac{12 \pm \sqrt{144 - 236}}{2} \end{aligned} $$ ## Simplify the radical expression $$ \begin{aligned} x &= \frac{12 \pm \sqrt{-92}}{2} \ x &= \frac{12 \pm \sqrt{4 \cdot 23 \cdot (-1)}}{2} \ x &= \frac{12 \pm 2i\sqrt{23}}{2} \ x &= 6 \pm \sqrt{23}i \end{aligned} $$

(A) $x = -12 \pm \sqrt{85}$

(B) $x = -6 \pm \sqrt{23}i$

(C) $x = 6 \pm \sqrt{23}i$

(D) $x = 12 \pm \sqrt{85}$

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

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Identify coefficients of the quadratic equation

Apply the quadratic formula

Simplify the radical expression

Answer: