solve.

\2x^2 + 6 = 0\

$x =$

(type exact answers, using radicals as needed. express complex numbers in terms of $i$. use a comma to separate answers.)

Question

solve.

\2x^2 + 6 = 0\

$x =$

(type exact answers, using radicals as needed. express complex numbers in terms of $i$. use a comma to separate answers.)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Solving Quadratic Equations", "Square Root Property", "Imaginary Numbers", "Simplifying Radicals" ], "new_concepts": [], "current_concepts": [ "Solving Quadratic Equations", "Square Root Property", "Imaginary Numbers", "Simplifying Radicals" ] } ## Isolate the quadratic term $$ \begin{aligned} 2x^2 + 6 &= 0 \ 2x^2 &= -6 \ x^2 &= -3 \end{aligned} $$ ## Apply the square root property $$ x = \pm\sqrt{-3} $$ ## Simplify using imaginary unit $$ x = \pm i\sqrt{3} $$ Solve. $2x^2 + 6 = 0$ $x =$ $i\sqrt{3}, -i\sqrt{3}$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Solving Quadratic Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Isolate the quadratic term

Apply the square root property

Simplify using imaginary unit

Answer: