Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(2x^2+10x=9x^2-4x\)
2. \(2x^2+15x=0\)
3. \(-4x^2+14x=0\)
4. \(5(7x^2+6x)=-(-39x^2-49x)\)
5. \(3(-9x^2-9x)=-(28x^2+38x)\)
6. \(2x^2-7x=-6x^2-5x\)
7. \(-4(-3x^2-10x)=-(-14x^2-26x)\)
8. \(5x^2-1x=0\)
9. \(-8x^2+13x=0\)
10. \(2x^2+12x=0\)
11. \(-5(8x^2+6x)=-(35x^2+21x)\)
12. \(-2(4x^2+9x)=-(15x^2+6x)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(2x^2+10x=9x^2-4x \\ \Leftrightarrow -7x^2+14x=0 \\ \Leftrightarrow x(-7x+14) = 0 \\ \Leftrightarrow x = 0 \vee -7x+14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-14}{-7} = 2 \\ V = \Big\{ 2; 0 \Big\} \\ -----------------\)
2. \(2x^2+15x=0 \\ \Leftrightarrow x(2x+15) = 0 \\ \Leftrightarrow x = 0 \vee 2x+15=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-15}{2} \\ V = \Big\{ 0 ; \frac{-15}{2} \Big\} \\ -----------------\)
3. \(-4x^2+14x=0 \\ \Leftrightarrow x(-4x+14) = 0 \\ \Leftrightarrow x = 0 \vee -4x+14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-14}{-4} = \frac{7}{2} \\ V = \Big\{ \frac{7}{2}; 0 \Big\} \\ -----------------\)
4. \(5(7x^2+6x)=-(-39x^2-49x) \\ \Leftrightarrow 35x^2+30x=39x^2+49x \\ \Leftrightarrow 35x^2+30x-39x^2-49x= 0 \\ \Leftrightarrow -4x^2+19x=0 \\ \Leftrightarrow x(-4x+19) = 0 \\ \Leftrightarrow x = 0 \vee -4x+19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-19}{-4} = \frac{19}{4} \\ V = \Big\{ \frac{19}{4}; 0 \Big\} \\ -----------------\)
5. \(3(-9x^2-9x)=-(28x^2+38x) \\ \Leftrightarrow -27x^2-27x=-28x^2-38x \\ \Leftrightarrow -27x^2-27x+28x^2+38x= 0 \\ \Leftrightarrow x^2-11x=0 \\ \Leftrightarrow x(x-11) = 0 \\ \Leftrightarrow x = 0 \vee x-11=0 \\ \Leftrightarrow x = 0 \vee x = \frac{11}{1} = 11 \\ V = \Big\{ 11; 0 \Big\} \\ -----------------\)
6. \(2x^2-7x=-6x^2-5x \\ \Leftrightarrow 8x^2-2x=0 \\ \Leftrightarrow x(8x-2) = 0 \\ \Leftrightarrow x = 0 \vee 8x-2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{2}{8} = \frac{1}{4} \\ V = \Big\{ \frac{1}{4}; 0 \Big\} \\ -----------------\)
7. \(-4(-3x^2-10x)=-(-14x^2-26x) \\ \Leftrightarrow 12x^2+40x=14x^2+26x \\ \Leftrightarrow 12x^2+40x-14x^2-26x= 0 \\ \Leftrightarrow -2x^2-14x=0 \\ \Leftrightarrow x(-2x-14) = 0 \\ \Leftrightarrow x = 0 \vee -2x-14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{14}{-2} = -7 \\ V = \Big\{ 0 ; -7 \Big\} \\ -----------------\)
8. \(5x^2-1x=0 \\ \Leftrightarrow x(5x-1) = 0 \\ \Leftrightarrow x = 0 \vee 5x-1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{1}{5} \\ V = \Big\{ \frac{1}{5}; 0 \Big\} \\ -----------------\)
9. \(-8x^2+13x=0 \\ \Leftrightarrow x(-8x+13) = 0 \\ \Leftrightarrow x = 0 \vee -8x+13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-13}{-8} = \frac{13}{8} \\ V = \Big\{ \frac{13}{8}; 0 \Big\} \\ -----------------\)
10. \(2x^2+12x=0 \\ \Leftrightarrow x(2x+12) = 0 \\ \Leftrightarrow x = 0 \vee 2x+12=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-12}{2} = -6 \\ V = \Big\{ 0 ; -6 \Big\} \\ -----------------\)
11. \(-5(8x^2+6x)=-(35x^2+21x) \\ \Leftrightarrow -40x^2-30x=-35x^2-21x \\ \Leftrightarrow -40x^2-30x+35x^2+21x= 0 \\ \Leftrightarrow -5x^2+9x=0 \\ \Leftrightarrow x(-5x+9) = 0 \\ \Leftrightarrow x = 0 \vee -5x+9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-9}{-5} = \frac{9}{5} \\ V = \Big\{ \frac{9}{5}; 0 \Big\} \\ -----------------\)
12. \(-2(4x^2+9x)=-(15x^2+6x) \\ \Leftrightarrow -8x^2-18x=-15x^2-6x \\ \Leftrightarrow -8x^2-18x+15x^2+6x= 0 \\ \Leftrightarrow 7x^2+12x=0 \\ \Leftrightarrow x(7x+12) = 0 \\ \Leftrightarrow x = 0 \vee 7x+12=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-12}{7} \\ V = \Big\{ 0 ; \frac{-12}{7} \Big\} \\ -----------------\)