Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-4(6x^2+2x)=-(29x^2-9x)\)
2. \(x^2-8x=7x^2-6x\)
3. \(13x^2-22x=10x^2-3x\)
4. \(2(-3x^2-10x)=-(x^2+21x)\)
5. \(-2x^2+13x=0\)
6. \(-2x^2-24x=-7x^2-4x\)
7. \(-3x^2-17x=-6x^2-4x\)
8. \(3x^2+6x=0\)
9. \(-5x^2+11x=0\)
10. \(3(-8x^2+9x)=-(26x^2-32x)\)
11. \(-2x^2-15x=-4x^2+6x\)
12. \(-4(5x^2-6x)=-(27x^2-40x)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-4(6x^2+2x)=-(29x^2-9x) \\ \Leftrightarrow -24x^2-8x=-29x^2+9x \\ \Leftrightarrow -24x^2-8x+29x^2-9x= 0 \\ \Leftrightarrow 5x^2+17x=0 \\ \Leftrightarrow x(5x+17) = 0 \\ \Leftrightarrow x = 0 \vee 5x+17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-17}{5} \\ V = \Big\{ 0 ; \frac{-17}{5} \Big\} \\ -----------------\)
2. \(x^2-8x=7x^2-6x \\ \Leftrightarrow -6x^2-2x=0 \\ \Leftrightarrow x(-6x-2) = 0 \\ \Leftrightarrow x = 0 \vee -6x-2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{2}{-6} = \frac{-1}{3} \\ V = \Big\{ 0 ; \frac{-1}{3} \Big\} \\ -----------------\)
3. \(13x^2-22x=10x^2-3x \\ \Leftrightarrow 3x^2-19x=0 \\ \Leftrightarrow x(3x-19) = 0 \\ \Leftrightarrow x = 0 \vee 3x-19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{19}{3} \\ V = \Big\{ \frac{19}{3}; 0 \Big\} \\ -----------------\)
4. \(2(-3x^2-10x)=-(x^2+21x) \\ \Leftrightarrow -6x^2-20x=-x^2-21x \\ \Leftrightarrow -6x^2-20x+x^2+21x= 0 \\ \Leftrightarrow -5x^2-1x=0 \\ \Leftrightarrow x(-5x-1) = 0 \\ \Leftrightarrow x = 0 \vee -5x-1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{1}{-5} = \frac{-1}{5} \\ V = \Big\{ 0 ; \frac{-1}{5} \Big\} \\ -----------------\)
5. \(-2x^2+13x=0 \\ \Leftrightarrow x(-2x+13) = 0 \\ \Leftrightarrow x = 0 \vee -2x+13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-13}{-2} = \frac{13}{2} \\ V = \Big\{ \frac{13}{2}; 0 \Big\} \\ -----------------\)
6. \(-2x^2-24x=-7x^2-4x \\ \Leftrightarrow 5x^2-20x=0 \\ \Leftrightarrow x(5x-20) = 0 \\ \Leftrightarrow x = 0 \vee 5x-20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{20}{5} = 4 \\ V = \Big\{ 4; 0 \Big\} \\ -----------------\)
7. \(-3x^2-17x=-6x^2-4x \\ \Leftrightarrow 3x^2-13x=0 \\ \Leftrightarrow x(3x-13) = 0 \\ \Leftrightarrow x = 0 \vee 3x-13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{13}{3} \\ V = \Big\{ \frac{13}{3}; 0 \Big\} \\ -----------------\)
8. \(3x^2+6x=0 \\ \Leftrightarrow x(3x+6) = 0 \\ \Leftrightarrow x = 0 \vee 3x+6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-6}{3} = -2 \\ V = \Big\{ 0 ; -2 \Big\} \\ -----------------\)
9. \(-5x^2+11x=0 \\ \Leftrightarrow x(-5x+11) = 0 \\ \Leftrightarrow x = 0 \vee -5x+11=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-11}{-5} = \frac{11}{5} \\ V = \Big\{ \frac{11}{5}; 0 \Big\} \\ -----------------\)
10. \(3(-8x^2+9x)=-(26x^2-32x) \\ \Leftrightarrow -24x^2+27x=-26x^2+32x \\ \Leftrightarrow -24x^2+27x+26x^2-32x= 0 \\ \Leftrightarrow 2x^2+5x=0 \\ \Leftrightarrow x(2x+5) = 0 \\ \Leftrightarrow x = 0 \vee 2x+5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-5}{2} \\ V = \Big\{ 0 ; \frac{-5}{2} \Big\} \\ -----------------\)
11. \(-2x^2-15x=-4x^2+6x \\ \Leftrightarrow 2x^2-21x=0 \\ \Leftrightarrow x(2x-21) = 0 \\ \Leftrightarrow x = 0 \vee 2x-21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{21}{2} \\ V = \Big\{ \frac{21}{2}; 0 \Big\} \\ -----------------\)
12. \(-4(5x^2-6x)=-(27x^2-40x) \\ \Leftrightarrow -20x^2+24x=-27x^2+40x \\ \Leftrightarrow -20x^2+24x+27x^2-40x= 0 \\ \Leftrightarrow 7x^2+16x=0 \\ \Leftrightarrow x(7x+16) = 0 \\ \Leftrightarrow x = 0 \vee 7x+16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-16}{7} \\ V = \Big\{ 0 ; \frac{-16}{7} \Big\} \\ -----------------\)