Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-3(7x^2+5x)=-(15x^2+5x)\)
2. \(-5x^2-10x=0\)
3. \(-4(4x^2-8x)=-(9x^2-9x)\)
4. \(x^2-10x=0\)
5. \(-14x^2-11x=-8x^2-3x\)
6. \(-5(-4x^2-9x)=-(-18x^2-46x)\)
7. \(-12x^2+16x=-9x^2+6x\)
8. \(3x^2+14x=0\)
9. \(2x^2-4x=0\)
10. \(-5x^2-21x=0\)
11. \(-10x^2+11x=-8x^2-5x\)
12. \(-5(7x^2-2x)=-(43x^2-7x)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-3(7x^2+5x)=-(15x^2+5x) \\ \Leftrightarrow -21x^2-15x=-15x^2-5x \\ \Leftrightarrow -21x^2-15x+15x^2+5x= 0 \\ \Leftrightarrow -6x^2+10x=0 \\ \Leftrightarrow x(-6x+10) = 0 \\ \Leftrightarrow x = 0 \vee -6x+10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-10}{-6} = \frac{5}{3} \\ V = \Big\{ \frac{5}{3}; 0 \Big\} \\ -----------------\)
2. \(-5x^2-10x=0 \\ \Leftrightarrow x(-5x-10) = 0 \\ \Leftrightarrow x = 0 \vee -5x-10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{10}{-5} = -2 \\ V = \Big\{ 0 ; -2 \Big\} \\ -----------------\)
3. \(-4(4x^2-8x)=-(9x^2-9x) \\ \Leftrightarrow -16x^2+32x=-9x^2+9x \\ \Leftrightarrow -16x^2+32x+9x^2-9x= 0 \\ \Leftrightarrow -7x^2-23x=0 \\ \Leftrightarrow x(-7x-23) = 0 \\ \Leftrightarrow x = 0 \vee -7x-23=0 \\ \Leftrightarrow x = 0 \vee x = \frac{23}{-7} = \frac{-23}{7} \\ V = \Big\{ 0 ; \frac{-23}{7} \Big\} \\ -----------------\)
4. \(x^2-10x=0 \\ \Leftrightarrow x(x-10) = 0 \\ \Leftrightarrow x = 0 \vee x-10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{10}{1} = 10 \\ V = \Big\{ 10; 0 \Big\} \\ -----------------\)
5. \(-14x^2-11x=-8x^2-3x \\ \Leftrightarrow -6x^2-8x=0 \\ \Leftrightarrow x(-6x-8) = 0 \\ \Leftrightarrow x = 0 \vee -6x-8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{8}{-6} = \frac{-4}{3} \\ V = \Big\{ 0 ; \frac{-4}{3} \Big\} \\ -----------------\)
6. \(-5(-4x^2-9x)=-(-18x^2-46x) \\ \Leftrightarrow 20x^2+45x=18x^2+46x \\ \Leftrightarrow 20x^2+45x-18x^2-46x= 0 \\ \Leftrightarrow 2x^2+1x=0 \\ \Leftrightarrow x(2x+1) = 0 \\ \Leftrightarrow x = 0 \vee 2x+1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-1}{2} \\ V = \Big\{ 0 ; \frac{-1}{2} \Big\} \\ -----------------\)
7. \(-12x^2+16x=-9x^2+6x \\ \Leftrightarrow -3x^2+10x=0 \\ \Leftrightarrow x(-3x+10) = 0 \\ \Leftrightarrow x = 0 \vee -3x+10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-10}{-3} = \frac{10}{3} \\ V = \Big\{ \frac{10}{3}; 0 \Big\} \\ -----------------\)
8. \(3x^2+14x=0 \\ \Leftrightarrow x(3x+14) = 0 \\ \Leftrightarrow x = 0 \vee 3x+14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-14}{3} \\ V = \Big\{ 0 ; \frac{-14}{3} \Big\} \\ -----------------\)
9. \(2x^2-4x=0 \\ \Leftrightarrow x(2x-4) = 0 \\ \Leftrightarrow x = 0 \vee 2x-4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{4}{2} = 2 \\ V = \Big\{ 2; 0 \Big\} \\ -----------------\)
10. \(-5x^2-21x=0 \\ \Leftrightarrow x(-5x-21) = 0 \\ \Leftrightarrow x = 0 \vee -5x-21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{21}{-5} = \frac{-21}{5} \\ V = \Big\{ 0 ; \frac{-21}{5} \Big\} \\ -----------------\)
11. \(-10x^2+11x=-8x^2-5x \\ \Leftrightarrow -2x^2+16x=0 \\ \Leftrightarrow x(-2x+16) = 0 \\ \Leftrightarrow x = 0 \vee -2x+16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-16}{-2} = 8 \\ V = \Big\{ 8; 0 \Big\} \\ -----------------\)
12. \(-5(7x^2-2x)=-(43x^2-7x) \\ \Leftrightarrow -35x^2+10x=-43x^2+7x \\ \Leftrightarrow -35x^2+10x+43x^2-7x= 0 \\ \Leftrightarrow 8x^2-3x=0 \\ \Leftrightarrow x(8x-3) = 0 \\ \Leftrightarrow x = 0 \vee 8x-3=0 \\ \Leftrightarrow x = 0 \vee x = \frac{3}{8} \\ V = \Big\{ \frac{3}{8}; 0 \Big\} \\ -----------------\)