Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-8x^2-22x=0\)
2. \(-3x^2-2x=0\)
3. \(-4x^2+15x=-3x^2+2x\)
4. \(-7x^2-x=-9x^2-2x\)
5. \(5(7x^2+6x)=-(-29x^2-13x)\)
6. \(-5x^2+2x=-7x^2+3x\)
7. \(x^2+31x=3x^2+9x\)
8. \(7x^2-25x=10x^2-10x\)
9. \(-2(9x^2-10x)=-(24x^2-27x)\)
10. \(-3x^2-16x=0\)
11. \(13x^2+11x=6x^2-4x\)
12. \(-12x^2-13x=-4x^2+5x\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-8x^2-22x=0 \\ \Leftrightarrow x(-8x-22) = 0 \\ \Leftrightarrow x = 0 \vee -8x-22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{22}{-8} = \frac{-11}{4} \\ V = \Big\{ 0 ; \frac{-11}{4} \Big\} \\ -----------------\)
2. \(-3x^2-2x=0 \\ \Leftrightarrow x(-3x-2) = 0 \\ \Leftrightarrow x = 0 \vee -3x-2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{2}{-3} = \frac{-2}{3} \\ V = \Big\{ 0 ; \frac{-2}{3} \Big\} \\ -----------------\)
3. \(-4x^2+15x=-3x^2+2x \\ \Leftrightarrow -x^2+13x=0 \\ \Leftrightarrow x(-x+13) = 0 \\ \Leftrightarrow x = 0 \vee -x+13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-13}{-1} = 13 \\ V = \Big\{ 13; 0 \Big\} \\ -----------------\)
4. \(-7x^2-x=-9x^2-2x \\ \Leftrightarrow 2x^2+1x=0 \\ \Leftrightarrow x(2x+1) = 0 \\ \Leftrightarrow x = 0 \vee 2x+1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-1}{2} \\ V = \Big\{ 0 ; \frac{-1}{2} \Big\} \\ -----------------\)
5. \(5(7x^2+6x)=-(-29x^2-13x) \\ \Leftrightarrow 35x^2+30x=29x^2+13x \\ \Leftrightarrow 35x^2+30x-29x^2-13x= 0 \\ \Leftrightarrow 6x^2-17x=0 \\ \Leftrightarrow x(6x-17) = 0 \\ \Leftrightarrow x = 0 \vee 6x-17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{17}{6} \\ V = \Big\{ \frac{17}{6}; 0 \Big\} \\ -----------------\)
6. \(-5x^2+2x=-7x^2+3x \\ \Leftrightarrow 2x^2-1x=0 \\ \Leftrightarrow x(2x-1) = 0 \\ \Leftrightarrow x = 0 \vee 2x-1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{1}{2} \\ V = \Big\{ \frac{1}{2}; 0 \Big\} \\ -----------------\)
7. \(x^2+31x=3x^2+9x \\ \Leftrightarrow -2x^2+22x=0 \\ \Leftrightarrow x(-2x+22) = 0 \\ \Leftrightarrow x = 0 \vee -2x+22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-22}{-2} = 11 \\ V = \Big\{ 11; 0 \Big\} \\ -----------------\)
8. \(7x^2-25x=10x^2-10x \\ \Leftrightarrow -3x^2-15x=0 \\ \Leftrightarrow x(-3x-15) = 0 \\ \Leftrightarrow x = 0 \vee -3x-15=0 \\ \Leftrightarrow x = 0 \vee x = \frac{15}{-3} = -5 \\ V = \Big\{ 0 ; -5 \Big\} \\ -----------------\)
9. \(-2(9x^2-10x)=-(24x^2-27x) \\ \Leftrightarrow -18x^2+20x=-24x^2+27x \\ \Leftrightarrow -18x^2+20x+24x^2-27x= 0 \\ \Leftrightarrow 6x^2+7x=0 \\ \Leftrightarrow x(6x+7) = 0 \\ \Leftrightarrow x = 0 \vee 6x+7=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-7}{6} \\ V = \Big\{ 0 ; \frac{-7}{6} \Big\} \\ -----------------\)
10. \(-3x^2-16x=0 \\ \Leftrightarrow x(-3x-16) = 0 \\ \Leftrightarrow x = 0 \vee -3x-16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{16}{-3} = \frac{-16}{3} \\ V = \Big\{ 0 ; \frac{-16}{3} \Big\} \\ -----------------\)
11. \(13x^2+11x=6x^2-4x \\ \Leftrightarrow 7x^2+15x=0 \\ \Leftrightarrow x(7x+15) = 0 \\ \Leftrightarrow x = 0 \vee 7x+15=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-15}{7} \\ V = \Big\{ 0 ; \frac{-15}{7} \Big\} \\ -----------------\)
12. \(-12x^2-13x=-4x^2+5x \\ \Leftrightarrow -8x^2-18x=0 \\ \Leftrightarrow x(-8x-18) = 0 \\ \Leftrightarrow x = 0 \vee -8x-18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{18}{-8} = \frac{-9}{4} \\ V = \Big\{ 0 ; \frac{-9}{4} \Big\} \\ -----------------\)