Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-5x^2-2x=0\)
2. \(-5x^2-10x=-3x^2+7x\)
3. \(x^2-22x=0\)
4. \(9x^2-25x=4x^2-6x\)
5. \(6x^2+4x=0\)
6. \(-4x^2-8x=-9x^2+9x\)
7. \(x^2+14x=-4x^2-3x\)
8. \(-3x^2+11x=0\)
9. \(5(10x^2-9x)=-(-47x^2+53x)\)
10. \(x^2+18x=8x^2-6x\)
11. \(3(10x^2-8x)=-(-31x^2+7x)\)
12. \(-11x^2-x=-4x^2-10x\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-5x^2-2x=0 \\ \Leftrightarrow x(-5x-2) = 0 \\ \Leftrightarrow x = 0 \vee -5x-2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{2}{-5} = \frac{-2}{5} \\ V = \Big\{ 0 ; \frac{-2}{5} \Big\} \\ -----------------\)
2. \(-5x^2-10x=-3x^2+7x \\ \Leftrightarrow -2x^2-17x=0 \\ \Leftrightarrow x(-2x-17) = 0 \\ \Leftrightarrow x = 0 \vee -2x-17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{17}{-2} = \frac{-17}{2} \\ V = \Big\{ 0 ; \frac{-17}{2} \Big\} \\ -----------------\)
3. \(x^2-22x=0 \\ \Leftrightarrow x(x-22) = 0 \\ \Leftrightarrow x = 0 \vee x-22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{22}{1} = 22 \\ V = \Big\{ 22; 0 \Big\} \\ -----------------\)
4. \(9x^2-25x=4x^2-6x \\ \Leftrightarrow 5x^2-19x=0 \\ \Leftrightarrow x(5x-19) = 0 \\ \Leftrightarrow x = 0 \vee 5x-19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{19}{5} \\ V = \Big\{ \frac{19}{5}; 0 \Big\} \\ -----------------\)
5. \(6x^2+4x=0 \\ \Leftrightarrow x(6x+4) = 0 \\ \Leftrightarrow x = 0 \vee 6x+4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-4}{6} = \frac{-2}{3} \\ V = \Big\{ 0 ; \frac{-2}{3} \Big\} \\ -----------------\)
6. \(-4x^2-8x=-9x^2+9x \\ \Leftrightarrow 5x^2-17x=0 \\ \Leftrightarrow x(5x-17) = 0 \\ \Leftrightarrow x = 0 \vee 5x-17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{17}{5} \\ V = \Big\{ \frac{17}{5}; 0 \Big\} \\ -----------------\)
7. \(x^2+14x=-4x^2-3x \\ \Leftrightarrow 5x^2+17x=0 \\ \Leftrightarrow x(5x+17) = 0 \\ \Leftrightarrow x = 0 \vee 5x+17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-17}{5} \\ V = \Big\{ 0 ; \frac{-17}{5} \Big\} \\ -----------------\)
8. \(-3x^2+11x=0 \\ \Leftrightarrow x(-3x+11) = 0 \\ \Leftrightarrow x = 0 \vee -3x+11=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-11}{-3} = \frac{11}{3} \\ V = \Big\{ \frac{11}{3}; 0 \Big\} \\ -----------------\)
9. \(5(10x^2-9x)=-(-47x^2+53x) \\ \Leftrightarrow 50x^2-45x=47x^2-53x \\ \Leftrightarrow 50x^2-45x-47x^2+53x= 0 \\ \Leftrightarrow 3x^2-8x=0 \\ \Leftrightarrow x(3x-8) = 0 \\ \Leftrightarrow x = 0 \vee 3x-8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{8}{3} \\ V = \Big\{ \frac{8}{3}; 0 \Big\} \\ -----------------\)
10. \(x^2+18x=8x^2-6x \\ \Leftrightarrow -7x^2+24x=0 \\ \Leftrightarrow x(-7x+24) = 0 \\ \Leftrightarrow x = 0 \vee -7x+24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-24}{-7} = \frac{24}{7} \\ V = \Big\{ \frac{24}{7}; 0 \Big\} \\ -----------------\)
11. \(3(10x^2-8x)=-(-31x^2+7x) \\ \Leftrightarrow 30x^2-24x=31x^2-7x \\ \Leftrightarrow 30x^2-24x-31x^2+7x= 0 \\ \Leftrightarrow -x^2+17x=0 \\ \Leftrightarrow x(-x+17) = 0 \\ \Leftrightarrow x = 0 \vee -x+17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-17}{-1} = 17 \\ V = \Big\{ 17; 0 \Big\} \\ -----------------\)
12. \(-11x^2-x=-4x^2-10x \\ \Leftrightarrow -7x^2+9x=0 \\ \Leftrightarrow x(-7x+9) = 0 \\ \Leftrightarrow x = 0 \vee -7x+9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-9}{-7} = \frac{9}{7} \\ V = \Big\{ \frac{9}{7}; 0 \Big\} \\ -----------------\)