question 2
drag the tiles to the correct boxes to complete the pairs.
solve each equation using the square root property. then, match the solutions to the equations they describe.

pairs
$x^2 + 81 = 0$
$x^2 - 22 = -26$
$3x^2 - 18 = 21$
$2x^2 + 15 = -13$

tiles
$\sqrt{13}, -\sqrt{13}$
$\sqrt{14}i, -\sqrt{14}i$
$9i, -9i$
$2i, -2i$

Question

question 2
drag the tiles to the correct boxes to complete the pairs.
solve each equation using the square root property. then, match the solutions to the equations they describe.

pairs
$x^2 + 81 = 0$
$x^2 - 22 = -26$
$3x^2 - 18 = 21$
$2x^2 + 15 = -13$

tiles
$\sqrt{13}, -\sqrt{13}$
$\sqrt{14}i, -\sqrt{14}i$
$9i, -9i$
$2i, -2i$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Square Root Property", "Complex Solutions" ], "current_concepts": [ "Solving Quadratic Equations", "Square Root Property", "Complex Solutions" ] } ## Solve the first equation $$ \begin{aligned} x^2 + 81 &= 0 \ x^2 &= -81 \ x &= \pm \sqrt{-81} \ x &= \pm 9i \end{aligned} $$ ## Solve the second equation $$ \begin{aligned} x^2 - 22 &= -26 \ x^2 &= -4 \ x &= \pm \sqrt{-4} \ x &= \pm 2i \end{aligned} $$ ## Solve the third and fourth equations $$ \begin{aligned} 3x^2 - 18 &= 21 \ 3x^2 &= 39 \ x^2 &= 13 \ x &= \pm \sqrt{13} \ \ 2x^2 + 15 &= -13 \ 2x^2 &= -28 \ x^2 &= -14 \ x &= \pm \sqrt{-14} \ x &= \pm \sqrt{14}i \end{aligned} $$ - $x^2 + 81 = 0$ matches with **$9i, -9i$** - $x^2 - 22 = -26$ matches with **$2i, -2i$** - $3x^2 - 18 = 21$ matches with **$\sqrt{13}, -\sqrt{13}$** - $2x^2 + 15 = -13$ matches with **$\sqrt{14}i, -\sqrt{14}i$** { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Solving Quadratic Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Solve the first equation

Solve the second equation

Solve the third and fourth equations

Answer: