solve: $2x^2 + 4x - 52 = 0$

(write your answers in the form $p + q\sqrt{r}$ and $p - q\sqrt{r}$)

Question

solve: $2x^2 + 4x - 52 = 0$

(write your answers in the form $p + q\sqrt{r}$ and $p - q\sqrt{r}$)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Quadratic Equations", "Quadratic Formula", "Radical Simplification" ], "new_concepts": [], "current_concepts": [ "Quadratic Equations", "Quadratic Formula", "Radical Simplification" ] } ## Divide the quadratic equation by the greatest common divisor $$ \begin{aligned} 2x^2 + 4x - 52 &= 0 \ x^2 + 2x - 26 &= 0 \end{aligned} $$ ## Apply the quadratic formula to solve for x $$ \begin{aligned} x &= \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \ x &= \frac{-2 \pm \sqrt{2^2 - 4(1)(-26)}}{2(1)} \ x &= \frac{-2 \pm \sqrt{4 + 104}}{2} \ x &= \frac{-2 \pm \sqrt{108}}{2} \end{aligned} $$ ## Simplify the radical expression and find the final values $$ \begin{aligned} \sqrt{108} &= \sqrt{36 \times 3} = 6\sqrt{3} \ x &= \frac{-2 \pm 6\sqrt{3}}{2} \ x &= -1 \pm 3\sqrt{3} \end{aligned} $$ $x = -1 + 3\sqrt{3}$ or $x = -1 - 3\sqrt{3}$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Quadratic Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Divide the quadratic equation by the greatest common divisor

Apply the quadratic formula to solve for x

Simplify the radical expression and find the final values

Answer: