Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-3x^2+16x=-10x^2-4x\)
2. \(5(5x^2+8x)=-(-18x^2-56x)\)
3. \(7x^2+25x=0\)
4. \(x^2+4x=0\)
5. \(-5x^2-4x=0\)
6. \(-7x^2+23x=0\)
7. \(13x^2-14x=10x^2-3x\)
8. \(-17x^2-17x=-10x^2+2x\)
9. \(2(4x^2+9x)=-(-14x^2-41x)\)
10. \(5(9x^2+7x)=-(-43x^2-55x)\)
11. \(5x^2+16x=0\)
12. \(-11x^2-16x=-8x^2+5x\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-3x^2+16x=-10x^2-4x \\ \Leftrightarrow 7x^2+20x=0 \\ \Leftrightarrow x(7x+20) = 0 \\ \Leftrightarrow x = 0 \vee 7x+20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-20}{7} \\ V = \Big\{ 0 ; \frac{-20}{7} \Big\} \\ -----------------\)
2. \(5(5x^2+8x)=-(-18x^2-56x) \\ \Leftrightarrow 25x^2+40x=18x^2+56x \\ \Leftrightarrow 25x^2+40x-18x^2-56x= 0 \\ \Leftrightarrow 7x^2+16x=0 \\ \Leftrightarrow x(7x+16) = 0 \\ \Leftrightarrow x = 0 \vee 7x+16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-16}{7} \\ V = \Big\{ 0 ; \frac{-16}{7} \Big\} \\ -----------------\)
3. \(7x^2+25x=0 \\ \Leftrightarrow x(7x+25) = 0 \\ \Leftrightarrow x = 0 \vee 7x+25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-25}{7} \\ V = \Big\{ 0 ; \frac{-25}{7} \Big\} \\ -----------------\)
4. \(x^2+4x=0 \\ \Leftrightarrow x(x+4) = 0 \\ \Leftrightarrow x = 0 \vee x+4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-4}{1} = -4 \\ V = \Big\{ 0 ; -4 \Big\} \\ -----------------\)
5. \(-5x^2-4x=0 \\ \Leftrightarrow x(-5x-4) = 0 \\ \Leftrightarrow x = 0 \vee -5x-4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{4}{-5} = \frac{-4}{5} \\ V = \Big\{ 0 ; \frac{-4}{5} \Big\} \\ -----------------\)
6. \(-7x^2+23x=0 \\ \Leftrightarrow x(-7x+23) = 0 \\ \Leftrightarrow x = 0 \vee -7x+23=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-23}{-7} = \frac{23}{7} \\ V = \Big\{ \frac{23}{7}; 0 \Big\} \\ -----------------\)
7. \(13x^2-14x=10x^2-3x \\ \Leftrightarrow 3x^2-11x=0 \\ \Leftrightarrow x(3x-11) = 0 \\ \Leftrightarrow x = 0 \vee 3x-11=0 \\ \Leftrightarrow x = 0 \vee x = \frac{11}{3} \\ V = \Big\{ \frac{11}{3}; 0 \Big\} \\ -----------------\)
8. \(-17x^2-17x=-10x^2+2x \\ \Leftrightarrow -7x^2-19x=0 \\ \Leftrightarrow x(-7x-19) = 0 \\ \Leftrightarrow x = 0 \vee -7x-19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{19}{-7} = \frac{-19}{7} \\ V = \Big\{ 0 ; \frac{-19}{7} \Big\} \\ -----------------\)
9. \(2(4x^2+9x)=-(-14x^2-41x) \\ \Leftrightarrow 8x^2+18x=14x^2+41x \\ \Leftrightarrow 8x^2+18x-14x^2-41x= 0 \\ \Leftrightarrow -6x^2+23x=0 \\ \Leftrightarrow x(-6x+23) = 0 \\ \Leftrightarrow x = 0 \vee -6x+23=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-23}{-6} = \frac{23}{6} \\ V = \Big\{ \frac{23}{6}; 0 \Big\} \\ -----------------\)
10. \(5(9x^2+7x)=-(-43x^2-55x) \\ \Leftrightarrow 45x^2+35x=43x^2+55x \\ \Leftrightarrow 45x^2+35x-43x^2-55x= 0 \\ \Leftrightarrow 2x^2+20x=0 \\ \Leftrightarrow x(2x+20) = 0 \\ \Leftrightarrow x = 0 \vee 2x+20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-20}{2} = -10 \\ V = \Big\{ 0 ; -10 \Big\} \\ -----------------\)
11. \(5x^2+16x=0 \\ \Leftrightarrow x(5x+16) = 0 \\ \Leftrightarrow x = 0 \vee 5x+16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-16}{5} \\ V = \Big\{ 0 ; \frac{-16}{5} \Big\} \\ -----------------\)
12. \(-11x^2-16x=-8x^2+5x \\ \Leftrightarrow -3x^2-21x=0 \\ \Leftrightarrow x(-3x-21) = 0 \\ \Leftrightarrow x = 0 \vee -3x-21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{21}{-3} = -7 \\ V = \Big\{ 0 ; -7 \Big\} \\ -----------------\)