Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(10x^2-24x=4x^2-10x\)
2. \(-5x^2-7x=-8x^2+9x\)
3. \(-x^2-32x=5x^2-9x\)
4. \(3(5x^2+3x)=-(-22x^2+0x)\)
5. \(6x^2-9x=0\)
6. \(-2(10x^2+9x)=-(12x^2-6x)\)
7. \(3(-2x^2+3x)=-(10x^2+15x)\)
8. \(8x^2+24x=9x^2+10x\)
9. \(-6x^2-21x=0\)
10. \(8x^2+19x=0\)
11. \(-x^2+27x=-8x^2+10x\)
12. \(-3x^2+18x=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(10x^2-24x=4x^2-10x \\ \Leftrightarrow 6x^2-14x=0 \\ \Leftrightarrow x(6x-14) = 0 \\ \Leftrightarrow x = 0 \vee 6x-14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{14}{6} = \frac{7}{3} \\ V = \Big\{ \frac{7}{3}; 0 \Big\} \\ -----------------\)
2. \(-5x^2-7x=-8x^2+9x \\ \Leftrightarrow 3x^2-16x=0 \\ \Leftrightarrow x(3x-16) = 0 \\ \Leftrightarrow x = 0 \vee 3x-16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{16}{3} \\ V = \Big\{ \frac{16}{3}; 0 \Big\} \\ -----------------\)
3. \(-x^2-32x=5x^2-9x \\ \Leftrightarrow -6x^2-23x=0 \\ \Leftrightarrow x(-6x-23) = 0 \\ \Leftrightarrow x = 0 \vee -6x-23=0 \\ \Leftrightarrow x = 0 \vee x = \frac{23}{-6} = \frac{-23}{6} \\ V = \Big\{ 0 ; \frac{-23}{6} \Big\} \\ -----------------\)
4. \(3(5x^2+3x)=-(-22x^2+0x) \\ \Leftrightarrow 15x^2+9x=22x^2+0x \\ \Leftrightarrow 15x^2+9x-22x^2+0x= 0 \\ \Leftrightarrow -7x^2-9x=0 \\ \Leftrightarrow x(-7x-9) = 0 \\ \Leftrightarrow x = 0 \vee -7x-9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{9}{-7} = \frac{-9}{7} \\ V = \Big\{ 0 ; \frac{-9}{7} \Big\} \\ -----------------\)
5. \(6x^2-9x=0 \\ \Leftrightarrow x(6x-9) = 0 \\ \Leftrightarrow x = 0 \vee 6x-9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{9}{6} = \frac{3}{2} \\ V = \Big\{ \frac{3}{2}; 0 \Big\} \\ -----------------\)
6. \(-2(10x^2+9x)=-(12x^2-6x) \\ \Leftrightarrow -20x^2-18x=-12x^2+6x \\ \Leftrightarrow -20x^2-18x+12x^2-6x= 0 \\ \Leftrightarrow -8x^2+24x=0 \\ \Leftrightarrow x(-8x+24) = 0 \\ \Leftrightarrow x = 0 \vee -8x+24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-24}{-8} = 3 \\ V = \Big\{ 3; 0 \Big\} \\ -----------------\)
7. \(3(-2x^2+3x)=-(10x^2+15x) \\ \Leftrightarrow -6x^2+9x=-10x^2-15x \\ \Leftrightarrow -6x^2+9x+10x^2+15x= 0 \\ \Leftrightarrow 4x^2-24x=0 \\ \Leftrightarrow x(4x-24) = 0 \\ \Leftrightarrow x = 0 \vee 4x-24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{24}{4} = 6 \\ V = \Big\{ 6; 0 \Big\} \\ -----------------\)
8. \(8x^2+24x=9x^2+10x \\ \Leftrightarrow -x^2+14x=0 \\ \Leftrightarrow x(-x+14) = 0 \\ \Leftrightarrow x = 0 \vee -x+14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-14}{-1} = 14 \\ V = \Big\{ 14; 0 \Big\} \\ -----------------\)
9. \(-6x^2-21x=0 \\ \Leftrightarrow x(-6x-21) = 0 \\ \Leftrightarrow x = 0 \vee -6x-21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{21}{-6} = \frac{-7}{2} \\ V = \Big\{ 0 ; \frac{-7}{2} \Big\} \\ -----------------\)
10. \(8x^2+19x=0 \\ \Leftrightarrow x(8x+19) = 0 \\ \Leftrightarrow x = 0 \vee 8x+19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-19}{8} \\ V = \Big\{ 0 ; \frac{-19}{8} \Big\} \\ -----------------\)
11. \(-x^2+27x=-8x^2+10x \\ \Leftrightarrow 7x^2+17x=0 \\ \Leftrightarrow x(7x+17) = 0 \\ \Leftrightarrow x = 0 \vee 7x+17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-17}{7} \\ V = \Big\{ 0 ; \frac{-17}{7} \Big\} \\ -----------------\)
12. \(-3x^2+18x=0 \\ \Leftrightarrow x(-3x+18) = 0 \\ \Leftrightarrow x = 0 \vee -3x+18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-18}{-3} = 6 \\ V = \Big\{ 6; 0 \Big\} \\ -----------------\)