using the quadratic formula to solve (x^2 + 20 = 2x), what are the values of (x)?

(1 pm sqrt{21}i)

(-1 pm sqrt{19}i)

(1 pm 2sqrt{19}i)

(1 pm sqrt{19}i)

Question

using the quadratic formula to solve (x^2 + 20 = 2x), what are the values of (x)?

(1 pm sqrt{21}i)

(-1 pm sqrt{19}i)

(1 pm 2sqrt{19}i)

(1 pm sqrt{19}i)

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 Formula Application", "Complex Numbers" ] } ## Rearrange the quadratic equation into standard form $$ \begin{aligned} x^2 + 20 &= 2x \ x^2 - 2x + 20 &= 0 \end{aligned} $$ ## Identify coefficients and apply the quadratic formula $$ \begin{aligned} a &= 1, \quad b = -2, \quad c = 20 \ x &= \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \ x &= \frac{-(-2) \pm \sqrt{(-2)^2 - 4(1)(20)}}{2(1)} \end{aligned} $$ ## Simplify the expression to find the values of x $$ \begin{aligned} x &= \frac{2 \pm \sqrt{4 - 80}}{2} \ x &= \frac{2 \pm \sqrt{-76}}{2} \ x &= \frac{2 \pm \sqrt{4 \times 19 \times (-1)}}{2} \ x &= \frac{2 \pm 2i\sqrt{19}}{2} \ x &= 1 \pm \sqrt{19}i \end{aligned} $$

(A) $1 \pm \sqrt{21}i$

(B) $-1 \pm \sqrt{19}i$

(C) $1 \pm 2\sqrt{19}i$

(D) $1 \pm \sqrt{19}i$

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

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QUESTION IMAGE

Question

Explanation:

Rearrange the quadratic equation into standard form

Identify coefficients and apply the quadratic formula

Simplify the expression to find the values of x

Answer: