Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(x^2-21x=3x^2-10x\)
2. \(4(4x^2+7x)=-(-18x^2-53x)\)
3. \(4x^2-4x=0\)
4. \(3(7x^2-3x)=-(-26x^2-10x)\)
5. \(x^2+8x=-3x^2-5x\)
6. \(-3(8x^2-5x)=-(22x^2-7x)\)
7. \(5(9x^2-6x)=-(-37x^2+9x)\)
8. \(-7x^2-18x=-6x^2+5x\)
9. \(10x^2-32x=9x^2-8x\)
10. \(-2x^2+12x=2x^2+2x\)
11. \(2x^2-14x=-5x^2+9x\)
12. \(5x^2+14x=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(x^2-21x=3x^2-10x \\ \Leftrightarrow -2x^2-11x=0 \\ \Leftrightarrow x(-2x-11) = 0 \\ \Leftrightarrow x = 0 \vee -2x-11=0 \\ \Leftrightarrow x = 0 \vee x = \frac{11}{-2} = \frac{-11}{2} \\ V = \Big\{ 0 ; \frac{-11}{2} \Big\} \\ -----------------\)
2. \(4(4x^2+7x)=-(-18x^2-53x) \\ \Leftrightarrow 16x^2+28x=18x^2+53x \\ \Leftrightarrow 16x^2+28x-18x^2-53x= 0 \\ \Leftrightarrow -2x^2+25x=0 \\ \Leftrightarrow x(-2x+25) = 0 \\ \Leftrightarrow x = 0 \vee -2x+25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-25}{-2} = \frac{25}{2} \\ V = \Big\{ \frac{25}{2}; 0 \Big\} \\ -----------------\)
3. \(4x^2-4x=0 \\ \Leftrightarrow x(4x-4) = 0 \\ \Leftrightarrow x = 0 \vee 4x-4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{4}{4} = 1 \\ V = \Big\{ 1; 0 \Big\} \\ -----------------\)
4. \(3(7x^2-3x)=-(-26x^2-10x) \\ \Leftrightarrow 21x^2-9x=26x^2+10x \\ \Leftrightarrow 21x^2-9x-26x^2-10x= 0 \\ \Leftrightarrow -5x^2+19x=0 \\ \Leftrightarrow x(-5x+19) = 0 \\ \Leftrightarrow x = 0 \vee -5x+19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-19}{-5} = \frac{19}{5} \\ V = \Big\{ \frac{19}{5}; 0 \Big\} \\ -----------------\)
5. \(x^2+8x=-3x^2-5x \\ \Leftrightarrow 4x^2+13x=0 \\ \Leftrightarrow x(4x+13) = 0 \\ \Leftrightarrow x = 0 \vee 4x+13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-13}{4} \\ V = \Big\{ 0 ; \frac{-13}{4} \Big\} \\ -----------------\)
6. \(-3(8x^2-5x)=-(22x^2-7x) \\ \Leftrightarrow -24x^2+15x=-22x^2+7x \\ \Leftrightarrow -24x^2+15x+22x^2-7x= 0 \\ \Leftrightarrow -2x^2-8x=0 \\ \Leftrightarrow x(-2x-8) = 0 \\ \Leftrightarrow x = 0 \vee -2x-8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{8}{-2} = -4 \\ V = \Big\{ 0 ; -4 \Big\} \\ -----------------\)
7. \(5(9x^2-6x)=-(-37x^2+9x) \\ \Leftrightarrow 45x^2-30x=37x^2-9x \\ \Leftrightarrow 45x^2-30x-37x^2+9x= 0 \\ \Leftrightarrow 8x^2+21x=0 \\ \Leftrightarrow x(8x+21) = 0 \\ \Leftrightarrow x = 0 \vee 8x+21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-21}{8} \\ V = \Big\{ 0 ; \frac{-21}{8} \Big\} \\ -----------------\)
8. \(-7x^2-18x=-6x^2+5x \\ \Leftrightarrow -x^2-23x=0 \\ \Leftrightarrow x(-x-23) = 0 \\ \Leftrightarrow x = 0 \vee -x-23=0 \\ \Leftrightarrow x = 0 \vee x = \frac{23}{-1} = -23 \\ V = \Big\{ 0 ; -23 \Big\} \\ -----------------\)
9. \(10x^2-32x=9x^2-8x \\ \Leftrightarrow x^2-24x=0 \\ \Leftrightarrow x(x-24) = 0 \\ \Leftrightarrow x = 0 \vee x-24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{24}{1} = 24 \\ V = \Big\{ 24; 0 \Big\} \\ -----------------\)
10. \(-2x^2+12x=2x^2+2x \\ \Leftrightarrow -4x^2+10x=0 \\ \Leftrightarrow x(-4x+10) = 0 \\ \Leftrightarrow x = 0 \vee -4x+10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-10}{-4} = \frac{5}{2} \\ V = \Big\{ \frac{5}{2}; 0 \Big\} \\ -----------------\)
11. \(2x^2-14x=-5x^2+9x \\ \Leftrightarrow 7x^2-23x=0 \\ \Leftrightarrow x(7x-23) = 0 \\ \Leftrightarrow x = 0 \vee 7x-23=0 \\ \Leftrightarrow x = 0 \vee x = \frac{23}{7} \\ V = \Big\{ \frac{23}{7}; 0 \Big\} \\ -----------------\)
12. \(5x^2+14x=0 \\ \Leftrightarrow x(5x+14) = 0 \\ \Leftrightarrow x = 0 \vee 5x+14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-14}{5} \\ V = \Big\{ 0 ; \frac{-14}{5} \Big\} \\ -----------------\)