Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-2x^2+18x=3x^2-6x\)
2. \(-4x^2-19x=0\)
3. \(6x^2-7x=10x^2-2x\)
4. \(7x^2-13x=0\)
5. \(-3(-5x^2+3x)=-(-14x^2+20x)\)
6. \(-9x^2+5x=-2x^2+7x\)
7. \(4x^2-18x=0\)
8. \(x^2+30x=3x^2+7x\)
9. \(-5(10x^2+10x)=-(54x^2+67x)\)
10. \(5x^2+7x=6x^2-6x\)
11. \(-2(-8x^2+8x)=-(-17x^2+37x)\)
12. \(-8x^2-24x=-5x^2-6x\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-2x^2+18x=3x^2-6x \\ \Leftrightarrow -5x^2+24x=0 \\ \Leftrightarrow x(-5x+24) = 0 \\ \Leftrightarrow x = 0 \vee -5x+24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-24}{-5} = \frac{24}{5} \\ V = \Big\{ \frac{24}{5}; 0 \Big\} \\ -----------------\)
2. \(-4x^2-19x=0 \\ \Leftrightarrow x(-4x-19) = 0 \\ \Leftrightarrow x = 0 \vee -4x-19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{19}{-4} = \frac{-19}{4} \\ V = \Big\{ 0 ; \frac{-19}{4} \Big\} \\ -----------------\)
3. \(6x^2-7x=10x^2-2x \\ \Leftrightarrow -4x^2-5x=0 \\ \Leftrightarrow x(-4x-5) = 0 \\ \Leftrightarrow x = 0 \vee -4x-5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{5}{-4} = \frac{-5}{4} \\ V = \Big\{ 0 ; \frac{-5}{4} \Big\} \\ -----------------\)
4. \(7x^2-13x=0 \\ \Leftrightarrow x(7x-13) = 0 \\ \Leftrightarrow x = 0 \vee 7x-13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{13}{7} \\ V = \Big\{ \frac{13}{7}; 0 \Big\} \\ -----------------\)
5. \(-3(-5x^2+3x)=-(-14x^2+20x) \\ \Leftrightarrow 15x^2-9x=14x^2-20x \\ \Leftrightarrow 15x^2-9x-14x^2+20x= 0 \\ \Leftrightarrow x^2-11x=0 \\ \Leftrightarrow x(x-11) = 0 \\ \Leftrightarrow x = 0 \vee x-11=0 \\ \Leftrightarrow x = 0 \vee x = \frac{11}{1} = 11 \\ V = \Big\{ 11; 0 \Big\} \\ -----------------\)
6. \(-9x^2+5x=-2x^2+7x \\ \Leftrightarrow -7x^2-2x=0 \\ \Leftrightarrow x(-7x-2) = 0 \\ \Leftrightarrow x = 0 \vee -7x-2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{2}{-7} = \frac{-2}{7} \\ V = \Big\{ 0 ; \frac{-2}{7} \Big\} \\ -----------------\)
7. \(4x^2-18x=0 \\ \Leftrightarrow x(4x-18) = 0 \\ \Leftrightarrow x = 0 \vee 4x-18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{18}{4} = \frac{9}{2} \\ V = \Big\{ \frac{9}{2}; 0 \Big\} \\ -----------------\)
8. \(x^2+30x=3x^2+7x \\ \Leftrightarrow -2x^2+23x=0 \\ \Leftrightarrow x(-2x+23) = 0 \\ \Leftrightarrow x = 0 \vee -2x+23=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-23}{-2} = \frac{23}{2} \\ V = \Big\{ \frac{23}{2}; 0 \Big\} \\ -----------------\)
9. \(-5(10x^2+10x)=-(54x^2+67x) \\ \Leftrightarrow -50x^2-50x=-54x^2-67x \\ \Leftrightarrow -50x^2-50x+54x^2+67x= 0 \\ \Leftrightarrow 4x^2-17x=0 \\ \Leftrightarrow x(4x-17) = 0 \\ \Leftrightarrow x = 0 \vee 4x-17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{17}{4} \\ V = \Big\{ \frac{17}{4}; 0 \Big\} \\ -----------------\)
10. \(5x^2+7x=6x^2-6x \\ \Leftrightarrow -x^2+13x=0 \\ \Leftrightarrow x(-x+13) = 0 \\ \Leftrightarrow x = 0 \vee -x+13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-13}{-1} = 13 \\ V = \Big\{ 13; 0 \Big\} \\ -----------------\)
11. \(-2(-8x^2+8x)=-(-17x^2+37x) \\ \Leftrightarrow 16x^2-16x=17x^2-37x \\ \Leftrightarrow 16x^2-16x-17x^2+37x= 0 \\ \Leftrightarrow -x^2-21x=0 \\ \Leftrightarrow x(-x-21) = 0 \\ \Leftrightarrow x = 0 \vee -x-21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{21}{-1} = -21 \\ V = \Big\{ 0 ; -21 \Big\} \\ -----------------\)
12. \(-8x^2-24x=-5x^2-6x \\ \Leftrightarrow -3x^2-18x=0 \\ \Leftrightarrow x(-3x-18) = 0 \\ \Leftrightarrow x = 0 \vee -3x-18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{18}{-3} = -6 \\ V = \Big\{ 0 ; -6 \Big\} \\ -----------------\)