Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-6x^2+2x=-9x^2-4x\)
2. \(7x^2+25x=3x^2+4x\)
3. \(7x^2+11x=6x^2+10x\)
4. \(-3(4x^2+7x)=-(15x^2+41x)\)
5. \(2x^2-5x=-3x^2-7x\)
6. \(-8x^2-10x=0\)
7. \(8x^2+12x=0\)
8. \(-4(5x^2+4x)=-(28x^2+10x)\)
9. \(2x^2+19x=10x^2-4x\)
10. \(-4(-10x^2-9x)=-(-37x^2-34x)\)
11. \(-5(-4x^2-4x)=-(-25x^2-36x)\)
12. \(-5x^2-5x=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-6x^2+2x=-9x^2-4x \\ \Leftrightarrow 3x^2+6x=0 \\ \Leftrightarrow x(3x+6) = 0 \\ \Leftrightarrow x = 0 \vee 3x+6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-6}{3} = -2 \\ V = \Big\{ 0 ; -2 \Big\} \\ -----------------\)
2. \(7x^2+25x=3x^2+4x \\ \Leftrightarrow 4x^2+21x=0 \\ \Leftrightarrow x(4x+21) = 0 \\ \Leftrightarrow x = 0 \vee 4x+21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-21}{4} \\ V = \Big\{ 0 ; \frac{-21}{4} \Big\} \\ -----------------\)
3. \(7x^2+11x=6x^2+10x \\ \Leftrightarrow x^2+1x=0 \\ \Leftrightarrow x(x+1) = 0 \\ \Leftrightarrow x = 0 \vee x+1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-1}{1} = -1 \\ V = \Big\{ 0 ; -1 \Big\} \\ -----------------\)
4. \(-3(4x^2+7x)=-(15x^2+41x) \\ \Leftrightarrow -12x^2-21x=-15x^2-41x \\ \Leftrightarrow -12x^2-21x+15x^2+41x= 0 \\ \Leftrightarrow 3x^2-20x=0 \\ \Leftrightarrow x(3x-20) = 0 \\ \Leftrightarrow x = 0 \vee 3x-20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{20}{3} \\ V = \Big\{ \frac{20}{3}; 0 \Big\} \\ -----------------\)
5. \(2x^2-5x=-3x^2-7x \\ \Leftrightarrow 5x^2+2x=0 \\ \Leftrightarrow x(5x+2) = 0 \\ \Leftrightarrow x = 0 \vee 5x+2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-2}{5} \\ V = \Big\{ 0 ; \frac{-2}{5} \Big\} \\ -----------------\)
6. \(-8x^2-10x=0 \\ \Leftrightarrow x(-8x-10) = 0 \\ \Leftrightarrow x = 0 \vee -8x-10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{10}{-8} = \frac{-5}{4} \\ V = \Big\{ 0 ; \frac{-5}{4} \Big\} \\ -----------------\)
7. \(8x^2+12x=0 \\ \Leftrightarrow x(8x+12) = 0 \\ \Leftrightarrow x = 0 \vee 8x+12=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-12}{8} = \frac{-3}{2} \\ V = \Big\{ 0 ; \frac{-3}{2} \Big\} \\ -----------------\)
8. \(-4(5x^2+4x)=-(28x^2+10x) \\ \Leftrightarrow -20x^2-16x=-28x^2-10x \\ \Leftrightarrow -20x^2-16x+28x^2+10x= 0 \\ \Leftrightarrow 8x^2+6x=0 \\ \Leftrightarrow x(8x+6) = 0 \\ \Leftrightarrow x = 0 \vee 8x+6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-6}{8} = \frac{-3}{4} \\ V = \Big\{ 0 ; \frac{-3}{4} \Big\} \\ -----------------\)
9. \(2x^2+19x=10x^2-4x \\ \Leftrightarrow -8x^2+23x=0 \\ \Leftrightarrow x(-8x+23) = 0 \\ \Leftrightarrow x = 0 \vee -8x+23=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-23}{-8} = \frac{23}{8} \\ V = \Big\{ \frac{23}{8}; 0 \Big\} \\ -----------------\)
10. \(-4(-10x^2-9x)=-(-37x^2-34x) \\ \Leftrightarrow 40x^2+36x=37x^2+34x \\ \Leftrightarrow 40x^2+36x-37x^2-34x= 0 \\ \Leftrightarrow 3x^2-2x=0 \\ \Leftrightarrow x(3x-2) = 0 \\ \Leftrightarrow x = 0 \vee 3x-2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{2}{3} \\ V = \Big\{ \frac{2}{3}; 0 \Big\} \\ -----------------\)
11. \(-5(-4x^2-4x)=-(-25x^2-36x) \\ \Leftrightarrow 20x^2+20x=25x^2+36x \\ \Leftrightarrow 20x^2+20x-25x^2-36x= 0 \\ \Leftrightarrow -5x^2+16x=0 \\ \Leftrightarrow x(-5x+16) = 0 \\ \Leftrightarrow x = 0 \vee -5x+16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-16}{-5} = \frac{16}{5} \\ V = \Big\{ \frac{16}{5}; 0 \Big\} \\ -----------------\)
12. \(-5x^2-5x=0 \\ \Leftrightarrow x(-5x-5) = 0 \\ \Leftrightarrow x = 0 \vee -5x-5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{5}{-5} = -1 \\ V = \Big\{ 0 ; -1 \Big\} \\ -----------------\)