Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-5x^2-2x=-10x^2-7x\)
2. \(-2x^2-8x=0\)
3. \(11x^2+5x=5x^2+3x\)
4. \(-7x^2-21x=0\)
5. \(3(4x^2-4x)=-(-19x^2-3x)\)
6. \(-15x^2-7x=-9x^2+10x\)
7. \(-4x^2+21x=0\)
8. \(-5x^2+5x=-6x^2+10x\)
9. \(-x^2+17x=0\)
10. \(-3(-8x^2-2x)=-(-29x^2-10x)\)
11. \(-2(8x^2-8x)=-(18x^2-20x)\)
12. \(2x^2+1x=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-5x^2-2x=-10x^2-7x \\ \Leftrightarrow 5x^2+5x=0 \\ \Leftrightarrow x(5x+5) = 0 \\ \Leftrightarrow x = 0 \vee 5x+5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-5}{5} = -1 \\ V = \Big\{ 0 ; -1 \Big\} \\ -----------------\)
2. \(-2x^2-8x=0 \\ \Leftrightarrow x(-2x-8) = 0 \\ \Leftrightarrow x = 0 \vee -2x-8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{8}{-2} = -4 \\ V = \Big\{ 0 ; -4 \Big\} \\ -----------------\)
3. \(11x^2+5x=5x^2+3x \\ \Leftrightarrow 6x^2+2x=0 \\ \Leftrightarrow x(6x+2) = 0 \\ \Leftrightarrow x = 0 \vee 6x+2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-2}{6} = \frac{-1}{3} \\ V = \Big\{ 0 ; \frac{-1}{3} \Big\} \\ -----------------\)
4. \(-7x^2-21x=0 \\ \Leftrightarrow x(-7x-21) = 0 \\ \Leftrightarrow x = 0 \vee -7x-21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{21}{-7} = -3 \\ V = \Big\{ 0 ; -3 \Big\} \\ -----------------\)
5. \(3(4x^2-4x)=-(-19x^2-3x) \\ \Leftrightarrow 12x^2-12x=19x^2+3x \\ \Leftrightarrow 12x^2-12x-19x^2-3x= 0 \\ \Leftrightarrow -7x^2+15x=0 \\ \Leftrightarrow x(-7x+15) = 0 \\ \Leftrightarrow x = 0 \vee -7x+15=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-15}{-7} = \frac{15}{7} \\ V = \Big\{ \frac{15}{7}; 0 \Big\} \\ -----------------\)
6. \(-15x^2-7x=-9x^2+10x \\ \Leftrightarrow -6x^2-17x=0 \\ \Leftrightarrow x(-6x-17) = 0 \\ \Leftrightarrow x = 0 \vee -6x-17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{17}{-6} = \frac{-17}{6} \\ V = \Big\{ 0 ; \frac{-17}{6} \Big\} \\ -----------------\)
7. \(-4x^2+21x=0 \\ \Leftrightarrow x(-4x+21) = 0 \\ \Leftrightarrow x = 0 \vee -4x+21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-21}{-4} = \frac{21}{4} \\ V = \Big\{ \frac{21}{4}; 0 \Big\} \\ -----------------\)
8. \(-5x^2+5x=-6x^2+10x \\ \Leftrightarrow x^2-5x=0 \\ \Leftrightarrow x(x-5) = 0 \\ \Leftrightarrow x = 0 \vee x-5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{5}{1} = 5 \\ V = \Big\{ 5; 0 \Big\} \\ -----------------\)
9. \(-x^2+17x=0 \\ \Leftrightarrow x(-x+17) = 0 \\ \Leftrightarrow x = 0 \vee -x+17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-17}{-1} = 17 \\ V = \Big\{ 17; 0 \Big\} \\ -----------------\)
10. \(-3(-8x^2-2x)=-(-29x^2-10x) \\ \Leftrightarrow 24x^2+6x=29x^2+10x \\ \Leftrightarrow 24x^2+6x-29x^2-10x= 0 \\ \Leftrightarrow -5x^2+4x=0 \\ \Leftrightarrow x(-5x+4) = 0 \\ \Leftrightarrow x = 0 \vee -5x+4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-4}{-5} = \frac{4}{5} \\ V = \Big\{ \frac{4}{5}; 0 \Big\} \\ -----------------\)
11. \(-2(8x^2-8x)=-(18x^2-20x) \\ \Leftrightarrow -16x^2+16x=-18x^2+20x \\ \Leftrightarrow -16x^2+16x+18x^2-20x= 0 \\ \Leftrightarrow 2x^2+4x=0 \\ \Leftrightarrow x(2x+4) = 0 \\ \Leftrightarrow x = 0 \vee 2x+4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-4}{2} = -2 \\ V = \Big\{ 0 ; -2 \Big\} \\ -----------------\)
12. \(2x^2+1x=0 \\ \Leftrightarrow x(2x+1) = 0 \\ \Leftrightarrow x = 0 \vee 2x+1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-1}{2} \\ V = \Big\{ 0 ; \frac{-1}{2} \Big\} \\ -----------------\)