Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-7x^2-21x=0\)
2. \(3(3x^2+3x)=-(-14x^2-18x)\)
3. \(-3x^2-16x=-10x^2+2x\)
4. \(-11x^2-4x=-3x^2-5x\)
5. \(5(9x^2+3x)=-(-39x^2-26x)\)
6. \(-4x^2-5x=0\)
7. \(-5(2x^2+5x)=-(15x^2+50x)\)
8. \(-7x^2-4x=-10x^2+6x\)
9. \(-3(6x^2-6x)=-(16x^2-14x)\)
10. \(2(4x^2+2x)=-(-13x^2+9x)\)
11. \(-8x^2+17x=0\)
12. \(-2x^2+12x=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-7x^2-21x=0 \\ \Leftrightarrow x(-7x-21) = 0 \\ \Leftrightarrow x = 0 \vee -7x-21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{21}{-7} = -3 \\ V = \Big\{ 0 ; -3 \Big\} \\ -----------------\)
2. \(3(3x^2+3x)=-(-14x^2-18x) \\ \Leftrightarrow 9x^2+9x=14x^2+18x \\ \Leftrightarrow 9x^2+9x-14x^2-18x= 0 \\ \Leftrightarrow -5x^2+9x=0 \\ \Leftrightarrow x(-5x+9) = 0 \\ \Leftrightarrow x = 0 \vee -5x+9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-9}{-5} = \frac{9}{5} \\ V = \Big\{ \frac{9}{5}; 0 \Big\} \\ -----------------\)
3. \(-3x^2-16x=-10x^2+2x \\ \Leftrightarrow 7x^2-18x=0 \\ \Leftrightarrow x(7x-18) = 0 \\ \Leftrightarrow x = 0 \vee 7x-18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{18}{7} \\ V = \Big\{ \frac{18}{7}; 0 \Big\} \\ -----------------\)
4. \(-11x^2-4x=-3x^2-5x \\ \Leftrightarrow -8x^2+1x=0 \\ \Leftrightarrow x(-8x+1) = 0 \\ \Leftrightarrow x = 0 \vee -8x+1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-1}{-8} = \frac{1}{8} \\ V = \Big\{ \frac{1}{8}; 0 \Big\} \\ -----------------\)
5. \(5(9x^2+3x)=-(-39x^2-26x) \\ \Leftrightarrow 45x^2+15x=39x^2+26x \\ \Leftrightarrow 45x^2+15x-39x^2-26x= 0 \\ \Leftrightarrow 6x^2+11x=0 \\ \Leftrightarrow x(6x+11) = 0 \\ \Leftrightarrow x = 0 \vee 6x+11=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-11}{6} \\ V = \Big\{ 0 ; \frac{-11}{6} \Big\} \\ -----------------\)
6. \(-4x^2-5x=0 \\ \Leftrightarrow x(-4x-5) = 0 \\ \Leftrightarrow x = 0 \vee -4x-5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{5}{-4} = \frac{-5}{4} \\ V = \Big\{ 0 ; \frac{-5}{4} \Big\} \\ -----------------\)
7. \(-5(2x^2+5x)=-(15x^2+50x) \\ \Leftrightarrow -10x^2-25x=-15x^2-50x \\ \Leftrightarrow -10x^2-25x+15x^2+50x= 0 \\ \Leftrightarrow 5x^2-25x=0 \\ \Leftrightarrow x(5x-25) = 0 \\ \Leftrightarrow x = 0 \vee 5x-25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{25}{5} = 5 \\ V = \Big\{ 5; 0 \Big\} \\ -----------------\)
8. \(-7x^2-4x=-10x^2+6x \\ \Leftrightarrow 3x^2-10x=0 \\ \Leftrightarrow x(3x-10) = 0 \\ \Leftrightarrow x = 0 \vee 3x-10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{10}{3} \\ V = \Big\{ \frac{10}{3}; 0 \Big\} \\ -----------------\)
9. \(-3(6x^2-6x)=-(16x^2-14x) \\ \Leftrightarrow -18x^2+18x=-16x^2+14x \\ \Leftrightarrow -18x^2+18x+16x^2-14x= 0 \\ \Leftrightarrow -2x^2-4x=0 \\ \Leftrightarrow x(-2x-4) = 0 \\ \Leftrightarrow x = 0 \vee -2x-4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{4}{-2} = -2 \\ V = \Big\{ 0 ; -2 \Big\} \\ -----------------\)
10. \(2(4x^2+2x)=-(-13x^2+9x) \\ \Leftrightarrow 8x^2+4x=13x^2-9x \\ \Leftrightarrow 8x^2+4x-13x^2+9x= 0 \\ \Leftrightarrow -5x^2-13x=0 \\ \Leftrightarrow x(-5x-13) = 0 \\ \Leftrightarrow x = 0 \vee -5x-13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{13}{-5} = \frac{-13}{5} \\ V = \Big\{ 0 ; \frac{-13}{5} \Big\} \\ -----------------\)
11. \(-8x^2+17x=0 \\ \Leftrightarrow x(-8x+17) = 0 \\ \Leftrightarrow x = 0 \vee -8x+17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-17}{-8} = \frac{17}{8} \\ V = \Big\{ \frac{17}{8}; 0 \Big\} \\ -----------------\)
12. \(-2x^2+12x=0 \\ \Leftrightarrow x(-2x+12) = 0 \\ \Leftrightarrow x = 0 \vee -2x+12=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-12}{-2} = 6 \\ V = \Big\{ 6; 0 \Big\} \\ -----------------\)