Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-4x^2-25x=0\)
2. \(-x^2-11x=0\)
3. \(x^2-19x=7x^2-9x\)
4. \(-3(7x^2-6x)=-(25x^2+2x)\)
5. \(-6x^2-21x=0\)
6. \(4(-3x^2+10x)=-(16x^2-28x)\)
7. \(-8x^2-14x=0\)
8. \(x^2+13x=6x^2-6x\)
9. \(-3(-8x^2+3x)=-(-25x^2+19x)\)
10. \(-4(-2x^2-9x)=-(-11x^2-46x)\)
11. \(10x^2-21x=2x^2-5x\)
12. \(-2x^2+4x=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-4x^2-25x=0 \\ \Leftrightarrow x(-4x-25) = 0 \\ \Leftrightarrow x = 0 \vee -4x-25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{25}{-4} = \frac{-25}{4} \\ V = \Big\{ 0 ; \frac{-25}{4} \Big\} \\ -----------------\)
2. \(-x^2-11x=0 \\ \Leftrightarrow x(-x-11) = 0 \\ \Leftrightarrow x = 0 \vee -x-11=0 \\ \Leftrightarrow x = 0 \vee x = \frac{11}{-1} = -11 \\ V = \Big\{ 0 ; -11 \Big\} \\ -----------------\)
3. \(x^2-19x=7x^2-9x \\ \Leftrightarrow -6x^2-10x=0 \\ \Leftrightarrow x(-6x-10) = 0 \\ \Leftrightarrow x = 0 \vee -6x-10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{10}{-6} = \frac{-5}{3} \\ V = \Big\{ 0 ; \frac{-5}{3} \Big\} \\ -----------------\)
4. \(-3(7x^2-6x)=-(25x^2+2x) \\ \Leftrightarrow -21x^2+18x=-25x^2-2x \\ \Leftrightarrow -21x^2+18x+25x^2+2x= 0 \\ \Leftrightarrow 4x^2-20x=0 \\ \Leftrightarrow x(4x-20) = 0 \\ \Leftrightarrow x = 0 \vee 4x-20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{20}{4} = 5 \\ V = \Big\{ 5; 0 \Big\} \\ -----------------\)
5. \(-6x^2-21x=0 \\ \Leftrightarrow x(-6x-21) = 0 \\ \Leftrightarrow x = 0 \vee -6x-21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{21}{-6} = \frac{-7}{2} \\ V = \Big\{ 0 ; \frac{-7}{2} \Big\} \\ -----------------\)
6. \(4(-3x^2+10x)=-(16x^2-28x) \\ \Leftrightarrow -12x^2+40x=-16x^2+28x \\ \Leftrightarrow -12x^2+40x+16x^2-28x= 0 \\ \Leftrightarrow 4x^2-12x=0 \\ \Leftrightarrow x(4x-12) = 0 \\ \Leftrightarrow x = 0 \vee 4x-12=0 \\ \Leftrightarrow x = 0 \vee x = \frac{12}{4} = 3 \\ V = \Big\{ 3; 0 \Big\} \\ -----------------\)
7. \(-8x^2-14x=0 \\ \Leftrightarrow x(-8x-14) = 0 \\ \Leftrightarrow x = 0 \vee -8x-14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{14}{-8} = \frac{-7}{4} \\ V = \Big\{ 0 ; \frac{-7}{4} \Big\} \\ -----------------\)
8. \(x^2+13x=6x^2-6x \\ \Leftrightarrow -5x^2+19x=0 \\ \Leftrightarrow x(-5x+19) = 0 \\ \Leftrightarrow x = 0 \vee -5x+19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-19}{-5} = \frac{19}{5} \\ V = \Big\{ \frac{19}{5}; 0 \Big\} \\ -----------------\)
9. \(-3(-8x^2+3x)=-(-25x^2+19x) \\ \Leftrightarrow 24x^2-9x=25x^2-19x \\ \Leftrightarrow 24x^2-9x-25x^2+19x= 0 \\ \Leftrightarrow -x^2-10x=0 \\ \Leftrightarrow x(-x-10) = 0 \\ \Leftrightarrow x = 0 \vee -x-10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{10}{-1} = -10 \\ V = \Big\{ 0 ; -10 \Big\} \\ -----------------\)
10. \(-4(-2x^2-9x)=-(-11x^2-46x) \\ \Leftrightarrow 8x^2+36x=11x^2+46x \\ \Leftrightarrow 8x^2+36x-11x^2-46x= 0 \\ \Leftrightarrow -3x^2+10x=0 \\ \Leftrightarrow x(-3x+10) = 0 \\ \Leftrightarrow x = 0 \vee -3x+10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-10}{-3} = \frac{10}{3} \\ V = \Big\{ \frac{10}{3}; 0 \Big\} \\ -----------------\)
11. \(10x^2-21x=2x^2-5x \\ \Leftrightarrow 8x^2-16x=0 \\ \Leftrightarrow x(8x-16) = 0 \\ \Leftrightarrow x = 0 \vee 8x-16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{16}{8} = 2 \\ V = \Big\{ 2; 0 \Big\} \\ -----------------\)
12. \(-2x^2+4x=0 \\ \Leftrightarrow x(-2x+4) = 0 \\ \Leftrightarrow x = 0 \vee -2x+4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-4}{-2} = 2 \\ V = \Big\{ 2; 0 \Big\} \\ -----------------\)