solve each of the quadratic equations

(3x = 0.5x^2)
- (x = -6) or (x = 0)
- (x = -4) or (x = 3)
- (x = -2) or (x = 1.5)
- (x = 0) or (x = 6)

(0 = 5x^2 - 2x + 6)
- (x = \frac{1 pm 3i}{2})
- (x = \frac{1 pm sqrt{11}}{5})
- (x = \frac{1 pm isqrt{29}}{5})

Question

solve each of the quadratic equations

(3x = 0.5x^2)
- (x = -6) or (x = 0)
- (x = -4) or (x = 3)
- (x = -2) or (x = 1.5)
- (x = 0) or (x = 6)

(0 = 5x^2 - 2x + 6)
- (x = \frac{1 pm 3i}{2})
- (x = \frac{1 pm sqrt{11}}{5})
- (x = \frac{1 pm isqrt{29}}{5})

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Solving Quadratic Equations" ], "new_concepts": [], "current_concepts": [ "Solving Quadratic Equations" ] } ## Solve the first quadratic equation $$ \begin{aligned} 3x &= 0.5x^2 \ 0.5x^2 - 3x &= 0 \ x(0.5x - 3) &= 0 \ x = 0 \quad &\text{or} \quad 0.5x - 3 = 0 \ x = 0 \quad &\text{or} \quad x = 6 \end{aligned} $$ ## Solve the second quadratic equation $$ \begin{aligned} 0 &= 5x^2 - 2x + 6 \ x &= \frac{-(-2) \pm \sqrt{(-2)^2 - 4(5)(6)}}{2(5)} \ x &= \frac{2 \pm \sqrt{4 - 120}}{10} \ x &= \frac{2 \pm \sqrt{-116}}{10} \ x &= \frac{2 \pm 2i\sqrt{29}}{10} \ x &= \frac{1 \pm i\sqrt{29}}{5} \end{aligned} $$ ## Question 1 $x = -6 \text{ or } x = 0$

$x = -4 \text{ or } x = 3$

$x = -2 \text{ or } x = 1.5$

$x = 0 \text{ or } x = 6$ ## Question 2 $x = \frac{1 \pm 3i}{2}$

$x = \frac{1 \pm \sqrt{11}}{5}$

$x = \frac{1 \pm i\sqrt{29}}{5}$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Solving Quadratic Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Solve the first quadratic equation

Solve the second quadratic equation

Answer:

Question 1

Question 2