Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(5(6x^2+7x)=-(-33x^2-49x)\)
2. \(-7x^2+3x=-6x^2-3x\)
3. \(3x^2-18x=0\)
4. \(-5(4x^2-9x)=-(12x^2-23x)\)
5. \(-8x^2+1x=0\)
6. \(-4x^2-5x=0\)
7. \(-5(-5x^2+10x)=-(-19x^2+63x)\)
8. \(8x^2+9x=0\)
9. \(-x^2+3x=0\)
10. \(3x^2+13x=5x^2-8x\)
11. \(5x^2-6x=0\)
12. \(2x^2+31x=7x^2+7x\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(5(6x^2+7x)=-(-33x^2-49x) \\ \Leftrightarrow 30x^2+35x=33x^2+49x \\ \Leftrightarrow 30x^2+35x-33x^2-49x= 0 \\ \Leftrightarrow -3x^2+14x=0 \\ \Leftrightarrow x(-3x+14) = 0 \\ \Leftrightarrow x = 0 \vee -3x+14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-14}{-3} = \frac{14}{3} \\ V = \Big\{ \frac{14}{3}; 0 \Big\} \\ -----------------\)
2. \(-7x^2+3x=-6x^2-3x \\ \Leftrightarrow -x^2+6x=0 \\ \Leftrightarrow x(-x+6) = 0 \\ \Leftrightarrow x = 0 \vee -x+6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-6}{-1} = 6 \\ V = \Big\{ 6; 0 \Big\} \\ -----------------\)
3. \(3x^2-18x=0 \\ \Leftrightarrow x(3x-18) = 0 \\ \Leftrightarrow x = 0 \vee 3x-18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{18}{3} = 6 \\ V = \Big\{ 6; 0 \Big\} \\ -----------------\)
4. \(-5(4x^2-9x)=-(12x^2-23x) \\ \Leftrightarrow -20x^2+45x=-12x^2+23x \\ \Leftrightarrow -20x^2+45x+12x^2-23x= 0 \\ \Leftrightarrow -8x^2-22x=0 \\ \Leftrightarrow x(-8x-22) = 0 \\ \Leftrightarrow x = 0 \vee -8x-22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{22}{-8} = \frac{-11}{4} \\ V = \Big\{ 0 ; \frac{-11}{4} \Big\} \\ -----------------\)
5. \(-8x^2+1x=0 \\ \Leftrightarrow x(-8x+1) = 0 \\ \Leftrightarrow x = 0 \vee -8x+1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-1}{-8} = \frac{1}{8} \\ V = \Big\{ \frac{1}{8}; 0 \Big\} \\ -----------------\)
6. \(-4x^2-5x=0 \\ \Leftrightarrow x(-4x-5) = 0 \\ \Leftrightarrow x = 0 \vee -4x-5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{5}{-4} = \frac{-5}{4} \\ V = \Big\{ 0 ; \frac{-5}{4} \Big\} \\ -----------------\)
7. \(-5(-5x^2+10x)=-(-19x^2+63x) \\ \Leftrightarrow 25x^2-50x=19x^2-63x \\ \Leftrightarrow 25x^2-50x-19x^2+63x= 0 \\ \Leftrightarrow 6x^2-13x=0 \\ \Leftrightarrow x(6x-13) = 0 \\ \Leftrightarrow x = 0 \vee 6x-13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{13}{6} \\ V = \Big\{ \frac{13}{6}; 0 \Big\} \\ -----------------\)
8. \(8x^2+9x=0 \\ \Leftrightarrow x(8x+9) = 0 \\ \Leftrightarrow x = 0 \vee 8x+9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-9}{8} \\ V = \Big\{ 0 ; \frac{-9}{8} \Big\} \\ -----------------\)
9. \(-x^2+3x=0 \\ \Leftrightarrow x(-x+3) = 0 \\ \Leftrightarrow x = 0 \vee -x+3=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-3}{-1} = 3 \\ V = \Big\{ 3; 0 \Big\} \\ -----------------\)
10. \(3x^2+13x=5x^2-8x \\ \Leftrightarrow -2x^2+21x=0 \\ \Leftrightarrow x(-2x+21) = 0 \\ \Leftrightarrow x = 0 \vee -2x+21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-21}{-2} = \frac{21}{2} \\ V = \Big\{ \frac{21}{2}; 0 \Big\} \\ -----------------\)
11. \(5x^2-6x=0 \\ \Leftrightarrow x(5x-6) = 0 \\ \Leftrightarrow x = 0 \vee 5x-6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{6}{5} \\ V = \Big\{ \frac{6}{5}; 0 \Big\} \\ -----------------\)
12. \(2x^2+31x=7x^2+7x \\ \Leftrightarrow -5x^2+24x=0 \\ \Leftrightarrow x(-5x+24) = 0 \\ \Leftrightarrow x = 0 \vee -5x+24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-24}{-5} = \frac{24}{5} \\ V = \Big\{ \frac{24}{5}; 0 \Big\} \\ -----------------\)