Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-17x^2+7x=-9x^2-7x\)
2. \(2x^2+9x=0\)
3. \(x^2+6x=-5x^2-2x\)
4. \(-8x^2+27x=-10x^2+4x\)
5. \(-11x^2-13x=-3x^2-2x\)
6. \(-4(9x^2+7x)=-(29x^2+19x)\)
7. \(x^2+11x=0\)
8. \(-2x^2-12x=-8x^2+5x\)
9. \(-3(-5x^2-7x)=-(-18x^2+3x)\)
10. \(11x^2-26x=4x^2-6x\)
11. \(4x^2+14x=-4x^2-6x\)
12. \(-4(6x^2-2x)=-(26x^2-21x)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-17x^2+7x=-9x^2-7x \\ \Leftrightarrow -8x^2+14x=0 \\ \Leftrightarrow x(-8x+14) = 0 \\ \Leftrightarrow x = 0 \vee -8x+14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-14}{-8} = \frac{7}{4} \\ V = \Big\{ \frac{7}{4}; 0 \Big\} \\ -----------------\)
2. \(2x^2+9x=0 \\ \Leftrightarrow x(2x+9) = 0 \\ \Leftrightarrow x = 0 \vee 2x+9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-9}{2} \\ V = \Big\{ 0 ; \frac{-9}{2} \Big\} \\ -----------------\)
3. \(x^2+6x=-5x^2-2x \\ \Leftrightarrow 6x^2+8x=0 \\ \Leftrightarrow x(6x+8) = 0 \\ \Leftrightarrow x = 0 \vee 6x+8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-8}{6} = \frac{-4}{3} \\ V = \Big\{ 0 ; \frac{-4}{3} \Big\} \\ -----------------\)
4. \(-8x^2+27x=-10x^2+4x \\ \Leftrightarrow 2x^2+23x=0 \\ \Leftrightarrow x(2x+23) = 0 \\ \Leftrightarrow x = 0 \vee 2x+23=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-23}{2} \\ V = \Big\{ 0 ; \frac{-23}{2} \Big\} \\ -----------------\)
5. \(-11x^2-13x=-3x^2-2x \\ \Leftrightarrow -8x^2-11x=0 \\ \Leftrightarrow x(-8x-11) = 0 \\ \Leftrightarrow x = 0 \vee -8x-11=0 \\ \Leftrightarrow x = 0 \vee x = \frac{11}{-8} = \frac{-11}{8} \\ V = \Big\{ 0 ; \frac{-11}{8} \Big\} \\ -----------------\)
6. \(-4(9x^2+7x)=-(29x^2+19x) \\ \Leftrightarrow -36x^2-28x=-29x^2-19x \\ \Leftrightarrow -36x^2-28x+29x^2+19x= 0 \\ \Leftrightarrow -7x^2+9x=0 \\ \Leftrightarrow x(-7x+9) = 0 \\ \Leftrightarrow x = 0 \vee -7x+9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-9}{-7} = \frac{9}{7} \\ V = \Big\{ \frac{9}{7}; 0 \Big\} \\ -----------------\)
7. \(x^2+11x=0 \\ \Leftrightarrow x(x+11) = 0 \\ \Leftrightarrow x = 0 \vee x+11=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-11}{1} = -11 \\ V = \Big\{ 0 ; -11 \Big\} \\ -----------------\)
8. \(-2x^2-12x=-8x^2+5x \\ \Leftrightarrow 6x^2-17x=0 \\ \Leftrightarrow x(6x-17) = 0 \\ \Leftrightarrow x = 0 \vee 6x-17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{17}{6} \\ V = \Big\{ \frac{17}{6}; 0 \Big\} \\ -----------------\)
9. \(-3(-5x^2-7x)=-(-18x^2+3x) \\ \Leftrightarrow 15x^2+21x=18x^2-3x \\ \Leftrightarrow 15x^2+21x-18x^2+3x= 0 \\ \Leftrightarrow -3x^2-24x=0 \\ \Leftrightarrow x(-3x-24) = 0 \\ \Leftrightarrow x = 0 \vee -3x-24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{24}{-3} = -8 \\ V = \Big\{ 0 ; -8 \Big\} \\ -----------------\)
10. \(11x^2-26x=4x^2-6x \\ \Leftrightarrow 7x^2-20x=0 \\ \Leftrightarrow x(7x-20) = 0 \\ \Leftrightarrow x = 0 \vee 7x-20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{20}{7} \\ V = \Big\{ \frac{20}{7}; 0 \Big\} \\ -----------------\)
11. \(4x^2+14x=-4x^2-6x \\ \Leftrightarrow 8x^2+20x=0 \\ \Leftrightarrow x(8x+20) = 0 \\ \Leftrightarrow x = 0 \vee 8x+20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-20}{8} = \frac{-5}{2} \\ V = \Big\{ 0 ; \frac{-5}{2} \Big\} \\ -----------------\)
12. \(-4(6x^2-2x)=-(26x^2-21x) \\ \Leftrightarrow -24x^2+8x=-26x^2+21x \\ \Leftrightarrow -24x^2+8x+26x^2-21x= 0 \\ \Leftrightarrow 2x^2+13x=0 \\ \Leftrightarrow x(2x+13) = 0 \\ \Leftrightarrow x = 0 \vee 2x+13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-13}{2} \\ V = \Big\{ 0 ; \frac{-13}{2} \Big\} \\ -----------------\)