Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(5x^2+5x=10x^2-9x\)
2. \(7x^2-10x=0\)
3. \(-5(7x^2+7x)=-(31x^2+23x)\)
4. \(x^2+16x=-2x^2+7x\)
5. \(7x^2-24x=0\)
6. \(2x^2-19x=9x^2+5x\)
7. \(-x^2+12x=4x^2-5x\)
8. \(2x^2+22x=9x^2+9x\)
9. \(7x^2-15x=6x^2-7x\)
10. \(5x^2-9x=0\)
11. \(x^2-13x=0\)
12. \(7x^2+16x=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(5x^2+5x=10x^2-9x \\ \Leftrightarrow -5x^2+14x=0 \\ \Leftrightarrow x(-5x+14) = 0 \\ \Leftrightarrow x = 0 \vee -5x+14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-14}{-5} = \frac{14}{5} \\ V = \Big\{ \frac{14}{5}; 0 \Big\} \\ -----------------\)
2. \(7x^2-10x=0 \\ \Leftrightarrow x(7x-10) = 0 \\ \Leftrightarrow x = 0 \vee 7x-10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{10}{7} \\ V = \Big\{ \frac{10}{7}; 0 \Big\} \\ -----------------\)
3. \(-5(7x^2+7x)=-(31x^2+23x) \\ \Leftrightarrow -35x^2-35x=-31x^2-23x \\ \Leftrightarrow -35x^2-35x+31x^2+23x= 0 \\ \Leftrightarrow -4x^2+12x=0 \\ \Leftrightarrow x(-4x+12) = 0 \\ \Leftrightarrow x = 0 \vee -4x+12=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-12}{-4} = 3 \\ V = \Big\{ 3; 0 \Big\} \\ -----------------\)
4. \(x^2+16x=-2x^2+7x \\ \Leftrightarrow 3x^2+9x=0 \\ \Leftrightarrow x(3x+9) = 0 \\ \Leftrightarrow x = 0 \vee 3x+9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-9}{3} = -3 \\ V = \Big\{ 0 ; -3 \Big\} \\ -----------------\)
5. \(7x^2-24x=0 \\ \Leftrightarrow x(7x-24) = 0 \\ \Leftrightarrow x = 0 \vee 7x-24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{24}{7} \\ V = \Big\{ \frac{24}{7}; 0 \Big\} \\ -----------------\)
6. \(2x^2-19x=9x^2+5x \\ \Leftrightarrow -7x^2-24x=0 \\ \Leftrightarrow x(-7x-24) = 0 \\ \Leftrightarrow x = 0 \vee -7x-24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{24}{-7} = \frac{-24}{7} \\ V = \Big\{ 0 ; \frac{-24}{7} \Big\} \\ -----------------\)
7. \(-x^2+12x=4x^2-5x \\ \Leftrightarrow -5x^2+17x=0 \\ \Leftrightarrow x(-5x+17) = 0 \\ \Leftrightarrow x = 0 \vee -5x+17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-17}{-5} = \frac{17}{5} \\ V = \Big\{ \frac{17}{5}; 0 \Big\} \\ -----------------\)
8. \(2x^2+22x=9x^2+9x \\ \Leftrightarrow -7x^2+13x=0 \\ \Leftrightarrow x(-7x+13) = 0 \\ \Leftrightarrow x = 0 \vee -7x+13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-13}{-7} = \frac{13}{7} \\ V = \Big\{ \frac{13}{7}; 0 \Big\} \\ -----------------\)
9. \(7x^2-15x=6x^2-7x \\ \Leftrightarrow x^2-8x=0 \\ \Leftrightarrow x(x-8) = 0 \\ \Leftrightarrow x = 0 \vee x-8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{8}{1} = 8 \\ V = \Big\{ 8; 0 \Big\} \\ -----------------\)
10. \(5x^2-9x=0 \\ \Leftrightarrow x(5x-9) = 0 \\ \Leftrightarrow x = 0 \vee 5x-9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{9}{5} \\ V = \Big\{ \frac{9}{5}; 0 \Big\} \\ -----------------\)
11. \(x^2-13x=0 \\ \Leftrightarrow x(x-13) = 0 \\ \Leftrightarrow x = 0 \vee x-13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{13}{1} = 13 \\ V = \Big\{ 13; 0 \Big\} \\ -----------------\)
12. \(7x^2+16x=0 \\ \Leftrightarrow x(7x+16) = 0 \\ \Leftrightarrow x = 0 \vee 7x+16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-16}{7} \\ V = \Big\{ 0 ; \frac{-16}{7} \Big\} \\ -----------------\)