$$ \begin{array}{ll} ext { (3) } x^{2}-3 x-2=0 ext { (wortelvorm) } & ext { (4) }-x^{2}-x=-5 ext { (wortelvorm) } \ ext { (5) }-x^{2}-5 x=2 ext { (wortelvorm) } & ext { (6) } \ x^{2}-11 x=-30 \ ext { (7) } x^{2}-12=0 ext { (wortelvorm) } & ext { (8) } \ ext { (9) } & -2 x^{2}+6 x=0 \ ext { (9) } 4 x^{2}-4 x-3=0 & ext { (10) } 3 x^{2}+8 x=-2 ext { (twee desima }\end{array} $$

Question

$$ \begin{array}{ll}	ext { (3) } x^{2}-3 x-2=0 	ext { (wortelvorm) } & 	ext { (4) }-x^{2}-x=-5 	ext { (wortelvorm) } \ 	ext { (5) }-x^{2}-5 x=2 	ext { (wortelvorm) } & 	ext { (6) } \ x^{2}-11 x=-30 \ 	ext { (7) } x^{2}-12=0 	ext { (wortelvorm) } & 	ext { (8) } \ 	ext { (9) } & -2 x^{2}+6 x=0 \ 	ext { (9) } 4 x^{2}-4 x-3=0 & 	ext { (10) } 3 x^{2}+8 x=-2 	ext { (twee desima }\end{array} $$

UpStudy AI · Accepted Answer

Natuurlijk, laten we de kwadratische vergelijkingen omzetten naar **wortelvorm** en de oplossingen berekenen. Hierbij geef ik zowel de exacte oplossingen als de benaderde waarden tot op twee decimalen.

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### (3) $$ x^{2} - 3x - 2 = 0 $$

**Wortelvorm:**
$$
x = \frac{3 \pm \sqrt{9 + 8}}{2} = \frac{3 \pm \sqrt{17}}{2}
$$

**Oplossingen:**
$$
x_1 = \frac{3 + \sqrt{17}}{2} \approx 3.56
$$
$$
x_2 = \frac{3 - \sqrt{17}}{2} \approx -0.56
$$

---

### (4) $$ -x^{2} - x = -5 $$

**Stappen:**
$$
-x^{2} - x + 5 = 0 \quad \Rightarrow \quad x^{2} + x - 5 = 0
$$

**Wortelvorm:**
$$
x = \frac{-1 \pm \sqrt{1 + 20}}{2} = \frac{-1 \pm \sqrt{21}}{2}
$$

**Oplossingen:**
$$
x_1 = \frac{-1 + \sqrt{21}}{2} \approx 1.79
$$
$$
x_2 = \frac{-1 - \sqrt{21}}{2} \approx -2.79
$$

---

### (5) $$ -x^{2} - 5x = 2 $$

**Stappen:**
$$
-x^{2} - 5x - 2 = 0 \quad \Rightarrow \quad x^{2} + 5x + 2 = 0
$$

**Wortelvorm:**
$$
x = \frac{-5 \pm \sqrt{25 - 8}}{2} = \frac{-5 \pm \sqrt{17}}{2}
$$

**Oplossingen:**
$$
x_1 = \frac{-5 + \sqrt{17}}{2} \approx -0.44
$$
$$
x_2 = \frac{-5 - \sqrt{17}}{2} \approx -4.56
$$

---

### (6)
*Er lijkt geen vergelijking te zijn opgegeven voor nummer 6.*

---

### (7) $$ x^{2} - 11x = -30 $$

**Stappen:**
$$
x^{2} - 11x + 30 = 0
$$

**Wortelvorm:**
$$
x = \frac{11 \pm \sqrt{121 - 120}}{2} = \frac{11 \pm 1}{2}
$$

**Oplossingen:**
$$
x_1 = \frac{12}{2} = 6
$$
$$
x_2 = \frac{10}{2} = 5
$$

---

### (8) $$ x^{2} - 12 = 0 $$

**Wortelvorm:**
$$
x = \pm \sqrt{12} = \pm 2\sqrt{3}
$$

**Oplossingen:**
$$
x_1 = 2\sqrt{3} \approx 3.46
$$
$$
x_2 = -2\sqrt{3} \approx -3.46
$$

---

### (9) $$ -2x^{2} + 6x = 0 $$

**Stappen:**
$$
-2x^{2} + 6x = 0 \quad \Rightarrow \quad -2x(x - 3) = 0
$$

**Oplossingen:**
$$
x = 0 \quad \text{of} \quad x = 3
$$

---

### (9) $$ 4x^{2} - 4x - 3 = 0 $$

**Wortelvorm:**
$$
x = \frac{4 \pm \sqrt{16 + 48}}{8} = \frac{4 \pm \sqrt{64}}{8} = \frac{4 \pm 8}{8}
$$

**Oplossingen:**
$$
x_1 = \frac{12}{8} = 1.5
$$
$$
x_2 = \frac{-4}{8} = -0.5
$$

---

### (10) $$ 3x^{2} + 8x = -2 $$

**Stappen:**
$$
3x^{2} + 8x + 2 = 0
$$

**Wortelvorm:**
$$
x = \frac{-8 \pm \sqrt{64 - 24}}{6} = \frac{-8 \pm \sqrt{40}}{6} = \frac{-8 \pm 2\sqrt{10}}{6} = \frac{-4 \pm \sqrt{10}}{3}
$$

**Oplossingen:**
$$
x_1 = \frac{-4 + \sqrt{10}}{3} \approx -0.28
$$
$$
x_2 = \frac{-4 - \sqrt{10}}{3} \approx -2.39
$$

---

Mocht je verdere verduidelijking nodig hebben of andere vragen hebben, laat het gerust weten!
Here are the solutions to the quadratic equations in the given list: 1. **(3) $$ x^{2} - 3x - 2 = 0 $$** - Solutions: $$ x \approx 3.56 $$ and $$ x \approx -0.56 $$ 2. **(4) $$ -x^{2} - x = -5 $$** - Solutions: $$ x \approx 1.79 $$ and $$ x \approx -2.79 $$ 3. **(5) $$ -x^{2} - 5x = 2 $$** - Solutions: $$ x \approx -0.44 $$ and $$ x \approx -4.56 $$ 4. **(6)** - No equation provided. 5. **(7) $$ x^{2} - 11x = -30 $$** - Solutions: $$ x = 6 $$ and $$ x = 5 $$ 6. **(8) $$ x^{2} - 12 = 0 $$** - Solutions: $$ x \approx 3.46 $$ and $$ x \approx -3.46 $$ 7. **(9) $$ -2x^{2} + 6x = 0 $$** - Solutions: $$ x = 0 $$ and $$ x = 3 $$ 8. **(9) $$ 4x^{2} - 4x - 3 = 0 $$** - Solutions: $$ x \approx 1.5 $$ and $$ x \approx -0.5 $$ 9. **(10) $$ 3x^{2} + 8x = -2 $$** - Solutions: $$ x \approx -0.28 $$ and $$ x \approx -2.39 $$ If you need further explanations or assistance with any of these solutions, feel free to ask!

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