Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(x^2-22x=-3x^2+2x\)
2. \(-5(-9x^2-5x)=-(-46x^2-43x)\)
3. \(4(7x^2-2x)=-(-22x^2+15x)\)
4. \(-8x^2-18x=0\)
5. \(6x^2-12x=0\)
6. \(5x^2+13x=0\)
7. \(8x^2-11x=0\)
8. \(7x^2+11x=2x^2+9x\)
9. \(5x^2-29x=8x^2-9x\)
10. \(-5x^2-6x=0\)
11. \(-x^2-21x=-9x^2-2x\)
12. \(2x^2+6x=-4x^2-4x\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(x^2-22x=-3x^2+2x \\ \Leftrightarrow 4x^2-24x=0 \\ \Leftrightarrow x(4x-24) = 0 \\ \Leftrightarrow x = 0 \vee 4x-24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{24}{4} = 6 \\ V = \Big\{ 6; 0 \Big\} \\ -----------------\)
2. \(-5(-9x^2-5x)=-(-46x^2-43x) \\ \Leftrightarrow 45x^2+25x=46x^2+43x \\ \Leftrightarrow 45x^2+25x-46x^2-43x= 0 \\ \Leftrightarrow -x^2+18x=0 \\ \Leftrightarrow x(-x+18) = 0 \\ \Leftrightarrow x = 0 \vee -x+18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-18}{-1} = 18 \\ V = \Big\{ 18; 0 \Big\} \\ -----------------\)
3. \(4(7x^2-2x)=-(-22x^2+15x) \\ \Leftrightarrow 28x^2-8x=22x^2-15x \\ \Leftrightarrow 28x^2-8x-22x^2+15x= 0 \\ \Leftrightarrow 6x^2-7x=0 \\ \Leftrightarrow x(6x-7) = 0 \\ \Leftrightarrow x = 0 \vee 6x-7=0 \\ \Leftrightarrow x = 0 \vee x = \frac{7}{6} \\ V = \Big\{ \frac{7}{6}; 0 \Big\} \\ -----------------\)
4. \(-8x^2-18x=0 \\ \Leftrightarrow x(-8x-18) = 0 \\ \Leftrightarrow x = 0 \vee -8x-18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{18}{-8} = \frac{-9}{4} \\ V = \Big\{ 0 ; \frac{-9}{4} \Big\} \\ -----------------\)
5. \(6x^2-12x=0 \\ \Leftrightarrow x(6x-12) = 0 \\ \Leftrightarrow x = 0 \vee 6x-12=0 \\ \Leftrightarrow x = 0 \vee x = \frac{12}{6} = 2 \\ V = \Big\{ 2; 0 \Big\} \\ -----------------\)
6. \(5x^2+13x=0 \\ \Leftrightarrow x(5x+13) = 0 \\ \Leftrightarrow x = 0 \vee 5x+13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-13}{5} \\ V = \Big\{ 0 ; \frac{-13}{5} \Big\} \\ -----------------\)
7. \(8x^2-11x=0 \\ \Leftrightarrow x(8x-11) = 0 \\ \Leftrightarrow x = 0 \vee 8x-11=0 \\ \Leftrightarrow x = 0 \vee x = \frac{11}{8} \\ V = \Big\{ \frac{11}{8}; 0 \Big\} \\ -----------------\)
8. \(7x^2+11x=2x^2+9x \\ \Leftrightarrow 5x^2+2x=0 \\ \Leftrightarrow x(5x+2) = 0 \\ \Leftrightarrow x = 0 \vee 5x+2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-2}{5} \\ V = \Big\{ 0 ; \frac{-2}{5} \Big\} \\ -----------------\)
9. \(5x^2-29x=8x^2-9x \\ \Leftrightarrow -3x^2-20x=0 \\ \Leftrightarrow x(-3x-20) = 0 \\ \Leftrightarrow x = 0 \vee -3x-20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{20}{-3} = \frac{-20}{3} \\ V = \Big\{ 0 ; \frac{-20}{3} \Big\} \\ -----------------\)
10. \(-5x^2-6x=0 \\ \Leftrightarrow x(-5x-6) = 0 \\ \Leftrightarrow x = 0 \vee -5x-6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{6}{-5} = \frac{-6}{5} \\ V = \Big\{ 0 ; \frac{-6}{5} \Big\} \\ -----------------\)
11. \(-x^2-21x=-9x^2-2x \\ \Leftrightarrow 8x^2-19x=0 \\ \Leftrightarrow x(8x-19) = 0 \\ \Leftrightarrow x = 0 \vee 8x-19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{19}{8} \\ V = \Big\{ \frac{19}{8}; 0 \Big\} \\ -----------------\)
12. \(2x^2+6x=-4x^2-4x \\ \Leftrightarrow 6x^2+10x=0 \\ \Leftrightarrow x(6x+10) = 0 \\ \Leftrightarrow x = 0 \vee 6x+10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-10}{6} = \frac{-5}{3} \\ V = \Big\{ 0 ; \frac{-5}{3} \Big\} \\ -----------------\)