Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(11x^2-20x=3x^2+5x\)
2. \(13x^2+x=8x^2-6x\)
3. \(4(7x^2+3x)=-(-32x^2+9x)\)
4. \(x^2-28x=-6x^2-9x\)
5. \(-2x^2+5x=0\)
6. \(-5(-4x^2+9x)=-(-28x^2+37x)\)
7. \(-5(8x^2+10x)=-(34x^2+64x)\)
8. \(x^2-x=8x^2+10x\)
9. \(-5(-4x^2+8x)=-(-18x^2+62x)\)
10. \(-4x^2+26x=4x^2+8x\)
11. \(-8x^2-21x=0\)
12. \(-4(-3x^2-2x)=-(-8x^2+0x)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(11x^2-20x=3x^2+5x \\ \Leftrightarrow 8x^2-25x=0 \\ \Leftrightarrow x(8x-25) = 0 \\ \Leftrightarrow x = 0 \vee 8x-25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{25}{8} \\ V = \Big\{ \frac{25}{8}; 0 \Big\} \\ -----------------\)
2. \(13x^2+x=8x^2-6x \\ \Leftrightarrow 5x^2+7x=0 \\ \Leftrightarrow x(5x+7) = 0 \\ \Leftrightarrow x = 0 \vee 5x+7=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-7}{5} \\ V = \Big\{ 0 ; \frac{-7}{5} \Big\} \\ -----------------\)
3. \(4(7x^2+3x)=-(-32x^2+9x) \\ \Leftrightarrow 28x^2+12x=32x^2-9x \\ \Leftrightarrow 28x^2+12x-32x^2+9x= 0 \\ \Leftrightarrow -4x^2-21x=0 \\ \Leftrightarrow x(-4x-21) = 0 \\ \Leftrightarrow x = 0 \vee -4x-21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{21}{-4} = \frac{-21}{4} \\ V = \Big\{ 0 ; \frac{-21}{4} \Big\} \\ -----------------\)
4. \(x^2-28x=-6x^2-9x \\ \Leftrightarrow 7x^2-19x=0 \\ \Leftrightarrow x(7x-19) = 0 \\ \Leftrightarrow x = 0 \vee 7x-19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{19}{7} \\ V = \Big\{ \frac{19}{7}; 0 \Big\} \\ -----------------\)
5. \(-2x^2+5x=0 \\ \Leftrightarrow x(-2x+5) = 0 \\ \Leftrightarrow x = 0 \vee -2x+5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-5}{-2} = \frac{5}{2} \\ V = \Big\{ \frac{5}{2}; 0 \Big\} \\ -----------------\)
6. \(-5(-4x^2+9x)=-(-28x^2+37x) \\ \Leftrightarrow 20x^2-45x=28x^2-37x \\ \Leftrightarrow 20x^2-45x-28x^2+37x= 0 \\ \Leftrightarrow -8x^2+8x=0 \\ \Leftrightarrow x(-8x+8) = 0 \\ \Leftrightarrow x = 0 \vee -8x+8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-8}{-8} = 1 \\ V = \Big\{ 1; 0 \Big\} \\ -----------------\)
7. \(-5(8x^2+10x)=-(34x^2+64x) \\ \Leftrightarrow -40x^2-50x=-34x^2-64x \\ \Leftrightarrow -40x^2-50x+34x^2+64x= 0 \\ \Leftrightarrow -6x^2-14x=0 \\ \Leftrightarrow x(-6x-14) = 0 \\ \Leftrightarrow x = 0 \vee -6x-14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{14}{-6} = \frac{-7}{3} \\ V = \Big\{ 0 ; \frac{-7}{3} \Big\} \\ -----------------\)
8. \(x^2-x=8x^2+10x \\ \Leftrightarrow -7x^2-11x=0 \\ \Leftrightarrow x(-7x-11) = 0 \\ \Leftrightarrow x = 0 \vee -7x-11=0 \\ \Leftrightarrow x = 0 \vee x = \frac{11}{-7} = \frac{-11}{7} \\ V = \Big\{ 0 ; \frac{-11}{7} \Big\} \\ -----------------\)
9. \(-5(-4x^2+8x)=-(-18x^2+62x) \\ \Leftrightarrow 20x^2-40x=18x^2-62x \\ \Leftrightarrow 20x^2-40x-18x^2+62x= 0 \\ \Leftrightarrow 2x^2-22x=0 \\ \Leftrightarrow x(2x-22) = 0 \\ \Leftrightarrow x = 0 \vee 2x-22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{22}{2} = 11 \\ V = \Big\{ 11; 0 \Big\} \\ -----------------\)
10. \(-4x^2+26x=4x^2+8x \\ \Leftrightarrow -8x^2+18x=0 \\ \Leftrightarrow x(-8x+18) = 0 \\ \Leftrightarrow x = 0 \vee -8x+18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-18}{-8} = \frac{9}{4} \\ V = \Big\{ \frac{9}{4}; 0 \Big\} \\ -----------------\)
11. \(-8x^2-21x=0 \\ \Leftrightarrow x(-8x-21) = 0 \\ \Leftrightarrow x = 0 \vee -8x-21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{21}{-8} = \frac{-21}{8} \\ V = \Big\{ 0 ; \frac{-21}{8} \Big\} \\ -----------------\)
12. \(-4(-3x^2-2x)=-(-8x^2+0x) \\ \Leftrightarrow 12x^2+8x=8x^2+0x \\ \Leftrightarrow 12x^2+8x-8x^2+0x= 0 \\ \Leftrightarrow 4x^2-8x=0 \\ \Leftrightarrow x(4x-8) = 0 \\ \Leftrightarrow x = 0 \vee 4x-8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{8}{4} = 2 \\ V = \Big\{ 2; 0 \Big\} \\ -----------------\)