enter the correct answer in the box.

what are the solutions of this quadratic equation?
\x^2 + 164 = 16x\

substitute the values of $a$ and $b$ to complete the solutions.

\x = a + bi\
\x = a - bi\

Question

enter the correct answer in the box.

what are the solutions of this quadratic equation?
\x^2 + 164 = 16x\

substitute the values of $a$ and $b$ to complete the solutions.

\x = a + bi\
\x = a - bi\

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Quadratic Formula Application", "Complex Number Arithmetic" ], "new_concepts": [], "current_concepts": [ "Quadratic Formula Application", "Complex Number Arithmetic", "Complex Conjugate Root Theorem" ] } ## Rearrange the quadratic equation into standard form $$ \begin{aligned} x^2 + 164 &= 16x \ x^2 - 16x + 164 &= 0 \end{aligned} $$ ## Apply the quadratic formula to find the roots $$ \begin{aligned} x &= \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \ x &= \frac{-(-16) \pm \sqrt{(-16)^2 - 4(1)(164)}}{2(1)} \ x &= \frac{16 \pm \sqrt{256 - 656}}{2} \ x &= \frac{16 \pm \sqrt{-400}}{2} \end{aligned} $$ ## Simplify the complex roots to find the values of a and b $$ \begin{aligned} x &= \frac{16 \pm 20i}{2} \ x &= 8 \pm 10i \end{aligned} $$ What are the solutions of this quadratic equation? $x^2 + 164 = 16x$ Substitute the values of a and b to complete the solutions. $x =$ $8 + 10i$ $x =$ $8 - 10i$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Quadratic Formula Application" ] }

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QUESTION IMAGE

Question

Explanation:

Rearrange the quadratic equation into standard form

Apply the quadratic formula to find the roots

Simplify the complex roots to find the values of a and b

Answer: