Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-9x^2-19x=-3x^2-2x\)
2. \(-5(3x^2+4x)=-(23x^2+29x)\)
3. \(-x^2-29x=-6x^2-6x\)
4. \(7x^2+9x=8x^2+10x\)
5. \(3(10x^2-7x)=-(-29x^2-3x)\)
6. \(5(-3x^2+5x)=-(20x^2-33x)\)
7. \(16x^2+6x=9x^2+7x\)
8. \(2x^2-1x=0\)
9. \(x^2-6x=-3x^2+10x\)
10. \(4x^2-13x=0\)
11. \(-11x^2+26x=-3x^2+5x\)
12. \(6x^2+11x=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-9x^2-19x=-3x^2-2x \\ \Leftrightarrow -6x^2-17x=0 \\ \Leftrightarrow x(-6x-17) = 0 \\ \Leftrightarrow x = 0 \vee -6x-17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{17}{-6} = \frac{-17}{6} \\ V = \Big\{ 0 ; \frac{-17}{6} \Big\} \\ -----------------\)
2. \(-5(3x^2+4x)=-(23x^2+29x) \\ \Leftrightarrow -15x^2-20x=-23x^2-29x \\ \Leftrightarrow -15x^2-20x+23x^2+29x= 0 \\ \Leftrightarrow 8x^2-9x=0 \\ \Leftrightarrow x(8x-9) = 0 \\ \Leftrightarrow x = 0 \vee 8x-9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{9}{8} \\ V = \Big\{ \frac{9}{8}; 0 \Big\} \\ -----------------\)
3. \(-x^2-29x=-6x^2-6x \\ \Leftrightarrow 5x^2-23x=0 \\ \Leftrightarrow x(5x-23) = 0 \\ \Leftrightarrow x = 0 \vee 5x-23=0 \\ \Leftrightarrow x = 0 \vee x = \frac{23}{5} \\ V = \Big\{ \frac{23}{5}; 0 \Big\} \\ -----------------\)
4. \(7x^2+9x=8x^2+10x \\ \Leftrightarrow -x^2-1x=0 \\ \Leftrightarrow x(-x-1) = 0 \\ \Leftrightarrow x = 0 \vee -x-1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{1}{-1} = -1 \\ V = \Big\{ 0 ; -1 \Big\} \\ -----------------\)
5. \(3(10x^2-7x)=-(-29x^2-3x) \\ \Leftrightarrow 30x^2-21x=29x^2+3x \\ \Leftrightarrow 30x^2-21x-29x^2-3x= 0 \\ \Leftrightarrow x^2+24x=0 \\ \Leftrightarrow x(x+24) = 0 \\ \Leftrightarrow x = 0 \vee x+24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-24}{1} = -24 \\ V = \Big\{ 0 ; -24 \Big\} \\ -----------------\)
6. \(5(-3x^2+5x)=-(20x^2-33x) \\ \Leftrightarrow -15x^2+25x=-20x^2+33x \\ \Leftrightarrow -15x^2+25x+20x^2-33x= 0 \\ \Leftrightarrow 5x^2+8x=0 \\ \Leftrightarrow x(5x+8) = 0 \\ \Leftrightarrow x = 0 \vee 5x+8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-8}{5} \\ V = \Big\{ 0 ; \frac{-8}{5} \Big\} \\ -----------------\)
7. \(16x^2+6x=9x^2+7x \\ \Leftrightarrow 7x^2-1x=0 \\ \Leftrightarrow x(7x-1) = 0 \\ \Leftrightarrow x = 0 \vee 7x-1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{1}{7} \\ V = \Big\{ \frac{1}{7}; 0 \Big\} \\ -----------------\)
8. \(2x^2-1x=0 \\ \Leftrightarrow x(2x-1) = 0 \\ \Leftrightarrow x = 0 \vee 2x-1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{1}{2} \\ V = \Big\{ \frac{1}{2}; 0 \Big\} \\ -----------------\)
9. \(x^2-6x=-3x^2+10x \\ \Leftrightarrow 4x^2-16x=0 \\ \Leftrightarrow x(4x-16) = 0 \\ \Leftrightarrow x = 0 \vee 4x-16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{16}{4} = 4 \\ V = \Big\{ 4; 0 \Big\} \\ -----------------\)
10. \(4x^2-13x=0 \\ \Leftrightarrow x(4x-13) = 0 \\ \Leftrightarrow x = 0 \vee 4x-13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{13}{4} \\ V = \Big\{ \frac{13}{4}; 0 \Big\} \\ -----------------\)
11. \(-11x^2+26x=-3x^2+5x \\ \Leftrightarrow -8x^2+21x=0 \\ \Leftrightarrow x(-8x+21) = 0 \\ \Leftrightarrow x = 0 \vee -8x+21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-21}{-8} = \frac{21}{8} \\ V = \Big\{ \frac{21}{8}; 0 \Big\} \\ -----------------\)
12. \(6x^2+11x=0 \\ \Leftrightarrow x(6x+11) = 0 \\ \Leftrightarrow x = 0 \vee 6x+11=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-11}{6} \\ V = \Big\{ 0 ; \frac{-11}{6} \Big\} \\ -----------------\)