Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(13x^2-x=8x^2-8x\)
2. \(-8x^2+25x=-3x^2+8x\)
3. \(-4(6x^2-10x)=-(23x^2-53x)\)
4. \(3x^2-16x=0\)
5. \(-6x^2+25x=-2x^2+6x\)
6. \(-6x^2+5x=-10x^2+5x\)
7. \(-2(-6x^2+8x)=-(-16x^2+36x)\)
8. \(-5(-4x^2+4x)=-(-23x^2-5x)\)
9. \(x^2-31x=-7x^2-10x\)
10. \(5(-4x^2+7x)=-(17x^2-57x)\)
11. \(3x^2+4x=0\)
12. \(-4(-2x^2-2x)=-(-15x^2+11x)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(13x^2-x=8x^2-8x \\ \Leftrightarrow 5x^2+7x=0 \\ \Leftrightarrow x(5x+7) = 0 \\ \Leftrightarrow x = 0 \vee 5x+7=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-7}{5} \\ V = \Big\{ 0 ; \frac{-7}{5} \Big\} \\ -----------------\)
2. \(-8x^2+25x=-3x^2+8x \\ \Leftrightarrow -5x^2+17x=0 \\ \Leftrightarrow x(-5x+17) = 0 \\ \Leftrightarrow x = 0 \vee -5x+17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-17}{-5} = \frac{17}{5} \\ V = \Big\{ \frac{17}{5}; 0 \Big\} \\ -----------------\)
3. \(-4(6x^2-10x)=-(23x^2-53x) \\ \Leftrightarrow -24x^2+40x=-23x^2+53x \\ \Leftrightarrow -24x^2+40x+23x^2-53x= 0 \\ \Leftrightarrow -x^2+13x=0 \\ \Leftrightarrow x(-x+13) = 0 \\ \Leftrightarrow x = 0 \vee -x+13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-13}{-1} = 13 \\ V = \Big\{ 13; 0 \Big\} \\ -----------------\)
4. \(3x^2-16x=0 \\ \Leftrightarrow x(3x-16) = 0 \\ \Leftrightarrow x = 0 \vee 3x-16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{16}{3} \\ V = \Big\{ \frac{16}{3}; 0 \Big\} \\ -----------------\)
5. \(-6x^2+25x=-2x^2+6x \\ \Leftrightarrow -4x^2+19x=0 \\ \Leftrightarrow x(-4x+19) = 0 \\ \Leftrightarrow x = 0 \vee -4x+19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-19}{-4} = \frac{19}{4} \\ V = \Big\{ \frac{19}{4}; 0 \Big\} \\ -----------------\)
6. \(-6x^2+5x=-10x^2+5x \\ \Leftrightarrow 4x^2+0x=0 \\ \Leftrightarrow 4x^2=0 \\ \Leftrightarrow x^2 = \frac{0}{4} \\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
7. \(-2(-6x^2+8x)=-(-16x^2+36x) \\ \Leftrightarrow 12x^2-16x=16x^2-36x \\ \Leftrightarrow 12x^2-16x-16x^2+36x= 0 \\ \Leftrightarrow -4x^2-20x=0 \\ \Leftrightarrow x(-4x-20) = 0 \\ \Leftrightarrow x = 0 \vee -4x-20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{20}{-4} = -5 \\ V = \Big\{ 0 ; -5 \Big\} \\ -----------------\)
8. \(-5(-4x^2+4x)=-(-23x^2-5x) \\ \Leftrightarrow 20x^2-20x=23x^2+5x \\ \Leftrightarrow 20x^2-20x-23x^2-5x= 0 \\ \Leftrightarrow -3x^2+25x=0 \\ \Leftrightarrow x(-3x+25) = 0 \\ \Leftrightarrow x = 0 \vee -3x+25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-25}{-3} = \frac{25}{3} \\ V = \Big\{ \frac{25}{3}; 0 \Big\} \\ -----------------\)
9. \(x^2-31x=-7x^2-10x \\ \Leftrightarrow 8x^2-21x=0 \\ \Leftrightarrow x(8x-21) = 0 \\ \Leftrightarrow x = 0 \vee 8x-21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{21}{8} \\ V = \Big\{ \frac{21}{8}; 0 \Big\} \\ -----------------\)
10. \(5(-4x^2+7x)=-(17x^2-57x) \\ \Leftrightarrow -20x^2+35x=-17x^2+57x \\ \Leftrightarrow -20x^2+35x+17x^2-57x= 0 \\ \Leftrightarrow -3x^2+22x=0 \\ \Leftrightarrow x(-3x+22) = 0 \\ \Leftrightarrow x = 0 \vee -3x+22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-22}{-3} = \frac{22}{3} \\ V = \Big\{ \frac{22}{3}; 0 \Big\} \\ -----------------\)
11. \(3x^2+4x=0 \\ \Leftrightarrow x(3x+4) = 0 \\ \Leftrightarrow x = 0 \vee 3x+4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-4}{3} \\ V = \Big\{ 0 ; \frac{-4}{3} \Big\} \\ -----------------\)
12. \(-4(-2x^2-2x)=-(-15x^2+11x) \\ \Leftrightarrow 8x^2+8x=15x^2-11x \\ \Leftrightarrow 8x^2+8x-15x^2+11x= 0 \\ \Leftrightarrow -7x^2-19x=0 \\ \Leftrightarrow x(-7x-19) = 0 \\ \Leftrightarrow x = 0 \vee -7x-19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{19}{-7} = \frac{-19}{7} \\ V = \Big\{ 0 ; \frac{-19}{7} \Big\} \\ -----------------\)