Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-5(6x^2+5x)=-(35x^2+32x)\)
2. \(2(-8x^2-9x)=-(21x^2+35x)\)
3. \(-x^2+22x=0\)
4. \(-11x^2+26x=-9x^2+10x\)
5. \(x^2-10x=0\)
6. \(6x^2-2x=0\)
7. \(4(-2x^2+3x)=-(7x^2-30x)\)
8. \(8x^2+22x=0\)
9. \(6x^2-31x=5x^2-7x\)
10. \(-11x^2+19x=-10x^2+5x\)
11. \(x^2+0x=0\)
12. \(-2(2x^2+10x)=-(11x^2+18x)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-5(6x^2+5x)=-(35x^2+32x) \\ \Leftrightarrow -30x^2-25x=-35x^2-32x \\ \Leftrightarrow -30x^2-25x+35x^2+32x= 0 \\ \Leftrightarrow 5x^2-7x=0 \\ \Leftrightarrow x(5x-7) = 0 \\ \Leftrightarrow x = 0 \vee 5x-7=0 \\ \Leftrightarrow x = 0 \vee x = \frac{7}{5} \\ V = \Big\{ \frac{7}{5}; 0 \Big\} \\ -----------------\)
2. \(2(-8x^2-9x)=-(21x^2+35x) \\ \Leftrightarrow -16x^2-18x=-21x^2-35x \\ \Leftrightarrow -16x^2-18x+21x^2+35x= 0 \\ \Leftrightarrow 5x^2-17x=0 \\ \Leftrightarrow x(5x-17) = 0 \\ \Leftrightarrow x = 0 \vee 5x-17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{17}{5} \\ V = \Big\{ \frac{17}{5}; 0 \Big\} \\ -----------------\)
3. \(-x^2+22x=0 \\ \Leftrightarrow x(-x+22) = 0 \\ \Leftrightarrow x = 0 \vee -x+22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-22}{-1} = 22 \\ V = \Big\{ 22; 0 \Big\} \\ -----------------\)
4. \(-11x^2+26x=-9x^2+10x \\ \Leftrightarrow -2x^2+16x=0 \\ \Leftrightarrow x(-2x+16) = 0 \\ \Leftrightarrow x = 0 \vee -2x+16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-16}{-2} = 8 \\ V = \Big\{ 8; 0 \Big\} \\ -----------------\)
5. \(x^2-10x=0 \\ \Leftrightarrow x(x-10) = 0 \\ \Leftrightarrow x = 0 \vee x-10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{10}{1} = 10 \\ V = \Big\{ 10; 0 \Big\} \\ -----------------\)
6. \(6x^2-2x=0 \\ \Leftrightarrow x(6x-2) = 0 \\ \Leftrightarrow x = 0 \vee 6x-2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{2}{6} = \frac{1}{3} \\ V = \Big\{ \frac{1}{3}; 0 \Big\} \\ -----------------\)
7. \(4(-2x^2+3x)=-(7x^2-30x) \\ \Leftrightarrow -8x^2+12x=-7x^2+30x \\ \Leftrightarrow -8x^2+12x+7x^2-30x= 0 \\ \Leftrightarrow -x^2+18x=0 \\ \Leftrightarrow x(-x+18) = 0 \\ \Leftrightarrow x = 0 \vee -x+18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-18}{-1} = 18 \\ V = \Big\{ 18; 0 \Big\} \\ -----------------\)
8. \(8x^2+22x=0 \\ \Leftrightarrow x(8x+22) = 0 \\ \Leftrightarrow x = 0 \vee 8x+22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-22}{8} = \frac{-11}{4} \\ V = \Big\{ 0 ; \frac{-11}{4} \Big\} \\ -----------------\)
9. \(6x^2-31x=5x^2-7x \\ \Leftrightarrow x^2-24x=0 \\ \Leftrightarrow x(x-24) = 0 \\ \Leftrightarrow x = 0 \vee x-24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{24}{1} = 24 \\ V = \Big\{ 24; 0 \Big\} \\ -----------------\)
10. \(-11x^2+19x=-10x^2+5x \\ \Leftrightarrow -x^2+14x=0 \\ \Leftrightarrow x(-x+14) = 0 \\ \Leftrightarrow x = 0 \vee -x+14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-14}{-1} = 14 \\ V = \Big\{ 14; 0 \Big\} \\ -----------------\)
11. \(x^2+0x=0 \\ \Leftrightarrow x^2=0 \\ \Leftrightarrow x^2 = \frac{0}{1} \\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
12. \(-2(2x^2+10x)=-(11x^2+18x) \\ \Leftrightarrow -4x^2-20x=-11x^2-18x \\ \Leftrightarrow -4x^2-20x+11x^2+18x= 0 \\ \Leftrightarrow 7x^2+2x=0 \\ \Leftrightarrow x(7x+2) = 0 \\ \Leftrightarrow x = 0 \vee 7x+2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-2}{7} \\ V = \Big\{ 0 ; \frac{-2}{7} \Big\} \\ -----------------\)