Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(5x^2-5x=3x^2+5x\)
2. \(17x^2+17x=10x^2+7x\)
3. \(3x^2+9x=0\)
4. \(-3(2x^2+3x)=-(7x^2+11x)\)
5. \(-11x^2-27x=-7x^2-10x\)
6. \(-7x^2+14x=0\)
7. \(4(-10x^2-2x)=-(38x^2-5x)\)
8. \(-3(10x^2-5x)=-(22x^2-18x)\)
9. \(8x^2-24x=0\)
10. \(2x^2-12x=0\)
11. \(3x^2-1x=0\)
12. \(-7x^2+29x=-4x^2+4x\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(5x^2-5x=3x^2+5x \\ \Leftrightarrow 2x^2-10x=0 \\ \Leftrightarrow x(2x-10) = 0 \\ \Leftrightarrow x = 0 \vee 2x-10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{10}{2} = 5 \\ V = \Big\{ 5; 0 \Big\} \\ -----------------\)
2. \(17x^2+17x=10x^2+7x \\ \Leftrightarrow 7x^2+10x=0 \\ \Leftrightarrow x(7x+10) = 0 \\ \Leftrightarrow x = 0 \vee 7x+10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-10}{7} \\ V = \Big\{ 0 ; \frac{-10}{7} \Big\} \\ -----------------\)
3. \(3x^2+9x=0 \\ \Leftrightarrow x(3x+9) = 0 \\ \Leftrightarrow x = 0 \vee 3x+9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-9}{3} = -3 \\ V = \Big\{ 0 ; -3 \Big\} \\ -----------------\)
4. \(-3(2x^2+3x)=-(7x^2+11x) \\ \Leftrightarrow -6x^2-9x=-7x^2-11x \\ \Leftrightarrow -6x^2-9x+7x^2+11x= 0 \\ \Leftrightarrow x^2-2x=0 \\ \Leftrightarrow x(x-2) = 0 \\ \Leftrightarrow x = 0 \vee x-2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{2}{1} = 2 \\ V = \Big\{ 2; 0 \Big\} \\ -----------------\)
5. \(-11x^2-27x=-7x^2-10x \\ \Leftrightarrow -4x^2-17x=0 \\ \Leftrightarrow x(-4x-17) = 0 \\ \Leftrightarrow x = 0 \vee -4x-17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{17}{-4} = \frac{-17}{4} \\ V = \Big\{ 0 ; \frac{-17}{4} \Big\} \\ -----------------\)
6. \(-7x^2+14x=0 \\ \Leftrightarrow x(-7x+14) = 0 \\ \Leftrightarrow x = 0 \vee -7x+14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-14}{-7} = 2 \\ V = \Big\{ 2; 0 \Big\} \\ -----------------\)
7. \(4(-10x^2-2x)=-(38x^2-5x) \\ \Leftrightarrow -40x^2-8x=-38x^2+5x \\ \Leftrightarrow -40x^2-8x+38x^2-5x= 0 \\ \Leftrightarrow -2x^2+13x=0 \\ \Leftrightarrow x(-2x+13) = 0 \\ \Leftrightarrow x = 0 \vee -2x+13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-13}{-2} = \frac{13}{2} \\ V = \Big\{ \frac{13}{2}; 0 \Big\} \\ -----------------\)
8. \(-3(10x^2-5x)=-(22x^2-18x) \\ \Leftrightarrow -30x^2+15x=-22x^2+18x \\ \Leftrightarrow -30x^2+15x+22x^2-18x= 0 \\ \Leftrightarrow -8x^2+3x=0 \\ \Leftrightarrow x(-8x+3) = 0 \\ \Leftrightarrow x = 0 \vee -8x+3=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-3}{-8} = \frac{3}{8} \\ V = \Big\{ \frac{3}{8}; 0 \Big\} \\ -----------------\)
9. \(8x^2-24x=0 \\ \Leftrightarrow x(8x-24) = 0 \\ \Leftrightarrow x = 0 \vee 8x-24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{24}{8} = 3 \\ V = \Big\{ 3; 0 \Big\} \\ -----------------\)
10. \(2x^2-12x=0 \\ \Leftrightarrow x(2x-12) = 0 \\ \Leftrightarrow x = 0 \vee 2x-12=0 \\ \Leftrightarrow x = 0 \vee x = \frac{12}{2} = 6 \\ V = \Big\{ 6; 0 \Big\} \\ -----------------\)
11. \(3x^2-1x=0 \\ \Leftrightarrow x(3x-1) = 0 \\ \Leftrightarrow x = 0 \vee 3x-1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{1}{3} \\ V = \Big\{ \frac{1}{3}; 0 \Big\} \\ -----------------\)
12. \(-7x^2+29x=-4x^2+4x \\ \Leftrightarrow -3x^2+25x=0 \\ \Leftrightarrow x(-3x+25) = 0 \\ \Leftrightarrow x = 0 \vee -3x+25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-25}{-3} = \frac{25}{3} \\ V = \Big\{ \frac{25}{3}; 0 \Big\} \\ -----------------\)