solve for $x$ using the square root property.

\2n^2 - 76 = -46\

$n =$

entry tip: do not use a decimal approximation for square roots. to enter a number like $5\sqrt{7}$, type 5*sqrt(7). preview your answer before submitting!

furthere tip: write your answers as a list, with your answers separated by (a) comma(s). for example, if you get 4 and $-\frac{2}{3}$ as your answers, then enter 4,-2/3 in the box.

Question

solve for $x$ using the square root property.

\2n^2 - 76 = -46\

$n =$

entry tip: do not use a decimal approximation for square roots. to enter a number like $5\sqrt{7}$, type 5*sqrt(7). preview your answer before submitting!

furthere tip: write your answers as a list, with your answers separated by (a) comma(s). for example, if you get 4 and $-\frac{2}{3}$ as your answers, then enter 4,-2/3 in the box.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Square Root Property", "Solving Quadratic Equations" ], "new_concepts": [], "current_concepts": [ "Square Root Property", "Solving Quadratic Equations", "Simplifying Radicals" ] } ## Isolate the quadratic term $$ \begin{aligned} 2n^2 - 76 &= -46 \ 2n^2 &= -46 + 76 \ 2n^2 &= 30 \end{aligned} $$ ## Divide by the coefficient $$ \begin{aligned} n^2 &= \frac{30}{2} \ n^2 &= 15 \end{aligned} $$ ## Apply the square root property $$ n = \pm\sqrt{15} $$ Solve for $x$ using the square root property. $2n^2 - 76 = -46$ $n =$ $\sqrt{15},-\sqrt{15}$ { "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

Divide by the coefficient

Apply the square root property

Answer: