# Onvolledige VKV (c=0)

#### Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. $$2(7x^2+2x)=-(-13x^2-10x)$$
2. $$-4x^2+27x=-10x^2+3x$$
3. $$-4x^2+14x=-9x^2+10x$$
4. $$-4(-3x^2-7x)=-(-20x^2-9x)$$
5. $$x^2+7x=8x^2-5x$$
6. $$9x^2-15x=2x^2-10x$$
7. $$-6x^2+19x=0$$
8. $$3(5x^2-3x)=-(-13x^2-9x)$$
9. $$-2x^2-19x=-4x^2+6x$$
10. $$7x^2-25x=0$$
11. $$-8x^2-8x=-7x^2+9x$$
12. $$8x^2+7x=6x^2+5x$$

#### Los de vierkantsvergelijking op zonder de discriminant te gebruiken

##### Verbetersleutel

1. $$2(7x^2+2x)=-(-13x^2-10x) \\ \Leftrightarrow 14x^2+4x=13x^2+10x \\ \Leftrightarrow 14x^2+4x-13x^2-10x= 0 \\ \Leftrightarrow x^2+6x=0 \\ \Leftrightarrow x(x-6) = 0 \\ \Leftrightarrow x = 0 \vee x-6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{6}{1} = 6 \\ V = \Big\{ 0 ; 6 \Big\} \\ -----------------$$
2. $$-4x^2+27x=-10x^2+3x \\ \Leftrightarrow 6x^2-24x=0 \\ \Leftrightarrow x(6x+24) = 0 \\ \Leftrightarrow x = 0 \vee 6x+24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-24}{6} = -4 \\ V = \Big\{ -4; 0 \Big\} \\ -----------------$$
3. $$-4x^2+14x=-9x^2+10x \\ \Leftrightarrow 5x^2-4x=0 \\ \Leftrightarrow x(5x+4) = 0 \\ \Leftrightarrow x = 0 \vee 5x+4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-4}{5} \\ V = \Big\{ \frac{-4}{5}; 0 \Big\} \\ -----------------$$
4. $$-4(-3x^2-7x)=-(-20x^2-9x) \\ \Leftrightarrow 12x^2+28x=20x^2+9x \\ \Leftrightarrow 12x^2+28x-20x^2-9x= 0 \\ \Leftrightarrow -8x^2-19x=0 \\ \Leftrightarrow x(-8x+19) = 0 \\ \Leftrightarrow x = 0 \vee -8x+19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-19}{-8} = \frac{19}{8} \\ V = \Big\{ 0 ; \frac{19}{8} \Big\} \\ -----------------$$
5. $$x^2+7x=8x^2-5x \\ \Leftrightarrow -7x^2-12x=0 \\ \Leftrightarrow x(-7x+12) = 0 \\ \Leftrightarrow x = 0 \vee -7x+12=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-12}{-7} = \frac{12}{7} \\ V = \Big\{ 0 ; \frac{12}{7} \Big\} \\ -----------------$$
6. $$9x^2-15x=2x^2-10x \\ \Leftrightarrow 7x^2+5x=0 \\ \Leftrightarrow x(7x-5) = 0 \\ \Leftrightarrow x = 0 \vee 7x-5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{5}{7} \\ V = \Big\{ 0 ; \frac{5}{7} \Big\} \\ -----------------$$
7. $$-6x^2+19x=0 \\ \Leftrightarrow x(-6x-19) = 0 \\ \Leftrightarrow x = 0 \vee -6x-19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{19}{-6} = \frac{-19}{6} \\ V = \Big\{ \frac{-19}{6}; 0 \Big\} \\ -----------------$$
8. $$3(5x^2-3x)=-(-13x^2-9x) \\ \Leftrightarrow 15x^2-9x=13x^2+9x \\ \Leftrightarrow 15x^2-9x-13x^2-9x= 0 \\ \Leftrightarrow 2x^2+18x=0 \\ \Leftrightarrow x(2x-18) = 0 \\ \Leftrightarrow x = 0 \vee 2x-18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{18}{2} = 9 \\ V = \Big\{ 0 ; 9 \Big\} \\ -----------------$$
9. $$-2x^2-19x=-4x^2+6x \\ \Leftrightarrow 2x^2+25x=0 \\ \Leftrightarrow x(2x-25) = 0 \\ \Leftrightarrow x = 0 \vee 2x-25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{25}{2} \\ V = \Big\{ 0 ; \frac{25}{2} \Big\} \\ -----------------$$
10. $$7x^2-25x=0 \\ \Leftrightarrow x(7x+25) = 0 \\ \Leftrightarrow x = 0 \vee 7x+25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-25}{7} \\ V = \Big\{ \frac{-25}{7}; 0 \Big\} \\ -----------------$$
11. $$-8x^2-8x=-7x^2+9x \\ \Leftrightarrow -x^2+17x=0 \\ \Leftrightarrow x(-x-17) = 0 \\ \Leftrightarrow x = 0 \vee -x-17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{17}{-1} = -17 \\ V = \Big\{ -17; 0 \Big\} \\ -----------------$$
12. $$8x^2+7x=6x^2+5x \\ \Leftrightarrow 2x^2-2x=0 \\ \Leftrightarrow x(2x+2) = 0 \\ \Leftrightarrow x = 0 \vee 2x+2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-2}{2} = -1 \\ V = \Big\{ -1; 0 \Big\} \\ -----------------$$
Oefeningengenerator vanhoeckes.be/wiskunde 2021-12-02 02:19:38