Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(3x^2+6x=-5x^2-8x\)
2. \(2x^2+4x=0\)
3. \(3x^2+10x=-3x^2-2x\)
4. \(-6x^2-10x=2x^2+8x\)
5. \(-5(5x^2-6x)=-(22x^2-29x)\)
6. \(4(8x^2-10x)=-(-27x^2+53x)\)
7. \(-5(9x^2-3x)=-(42x^2+4x)\)
8. \(9x^2-30x=2x^2-5x\)
9. \(4(3x^2-6x)=-(-20x^2+47x)\)
10. \(12x^2+3x=4x^2+7x\)
11. \(-2x^2-7x=0\)
12. \(9x^2-7x=4x^2-5x\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(3x^2+6x=-5x^2-8x \\ \Leftrightarrow 8x^2+14x=0 \\ \Leftrightarrow x(8x+14) = 0 \\ \Leftrightarrow x = 0 \vee 8x+14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-14}{8} = \frac{-7}{4} \\ V = \Big\{ 0 ; \frac{-7}{4} \Big\} \\ -----------------\)
2. \(2x^2+4x=0 \\ \Leftrightarrow x(2x+4) = 0 \\ \Leftrightarrow x = 0 \vee 2x+4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-4}{2} = -2 \\ V = \Big\{ 0 ; -2 \Big\} \\ -----------------\)
3. \(3x^2+10x=-3x^2-2x \\ \Leftrightarrow 6x^2+12x=0 \\ \Leftrightarrow x(6x+12) = 0 \\ \Leftrightarrow x = 0 \vee 6x+12=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-12}{6} = -2 \\ V = \Big\{ 0 ; -2 \Big\} \\ -----------------\)
4. \(-6x^2-10x=2x^2+8x \\ \Leftrightarrow -8x^2-18x=0 \\ \Leftrightarrow x(-8x-18) = 0 \\ \Leftrightarrow x = 0 \vee -8x-18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{18}{-8} = \frac{-9}{4} \\ V = \Big\{ 0 ; \frac{-9}{4} \Big\} \\ -----------------\)
5. \(-5(5x^2-6x)=-(22x^2-29x) \\ \Leftrightarrow -25x^2+30x=-22x^2+29x \\ \Leftrightarrow -25x^2+30x+22x^2-29x= 0 \\ \Leftrightarrow -3x^2-1x=0 \\ \Leftrightarrow x(-3x-1) = 0 \\ \Leftrightarrow x = 0 \vee -3x-1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{1}{-3} = \frac{-1}{3} \\ V = \Big\{ 0 ; \frac{-1}{3} \Big\} \\ -----------------\)
6. \(4(8x^2-10x)=-(-27x^2+53x) \\ \Leftrightarrow 32x^2-40x=27x^2-53x \\ \Leftrightarrow 32x^2-40x-27x^2+53x= 0 \\ \Leftrightarrow 5x^2-13x=0 \\ \Leftrightarrow x(5x-13) = 0 \\ \Leftrightarrow x = 0 \vee 5x-13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{13}{5} \\ V = \Big\{ \frac{13}{5}; 0 \Big\} \\ -----------------\)
7. \(-5(9x^2-3x)=-(42x^2+4x) \\ \Leftrightarrow -45x^2+15x=-42x^2-4x \\ \Leftrightarrow -45x^2+15x+42x^2+4x= 0 \\ \Leftrightarrow -3x^2-19x=0 \\ \Leftrightarrow x(-3x-19) = 0 \\ \Leftrightarrow x = 0 \vee -3x-19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{19}{-3} = \frac{-19}{3} \\ V = \Big\{ 0 ; \frac{-19}{3} \Big\} \\ -----------------\)
8. \(9x^2-30x=2x^2-5x \\ \Leftrightarrow 7x^2-25x=0 \\ \Leftrightarrow x(7x-25) = 0 \\ \Leftrightarrow x = 0 \vee 7x-25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{25}{7} \\ V = \Big\{ \frac{25}{7}; 0 \Big\} \\ -----------------\)
9. \(4(3x^2-6x)=-(-20x^2+47x) \\ \Leftrightarrow 12x^2-24x=20x^2-47x \\ \Leftrightarrow 12x^2-24x-20x^2+47x= 0 \\ \Leftrightarrow -8x^2-23x=0 \\ \Leftrightarrow x(-8x-23) = 0 \\ \Leftrightarrow x = 0 \vee -8x-23=0 \\ \Leftrightarrow x = 0 \vee x = \frac{23}{-8} = \frac{-23}{8} \\ V = \Big\{ 0 ; \frac{-23}{8} \Big\} \\ -----------------\)
10. \(12x^2+3x=4x^2+7x \\ \Leftrightarrow 8x^2-4x=0 \\ \Leftrightarrow x(8x-4) = 0 \\ \Leftrightarrow x = 0 \vee 8x-4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{4}{8} = \frac{1}{2} \\ V = \Big\{ \frac{1}{2}; 0 \Big\} \\ -----------------\)
11. \(-2x^2-7x=0 \\ \Leftrightarrow x(-2x-7) = 0 \\ \Leftrightarrow x = 0 \vee -2x-7=0 \\ \Leftrightarrow x = 0 \vee x = \frac{7}{-2} = \frac{-7}{2} \\ V = \Big\{ 0 ; \frac{-7}{2} \Big\} \\ -----------------\)
12. \(9x^2-7x=4x^2-5x \\ \Leftrightarrow 5x^2-2x=0 \\ \Leftrightarrow x(5x-2) = 0 \\ \Leftrightarrow x = 0 \vee 5x-2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{2}{5} \\ V = \Big\{ \frac{2}{5}; 0 \Big\} \\ -----------------\)