Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(8x^2+11x=0\)
2. \(-4(-5x^2+7x)=-(-21x^2+52x)\)
3. \(5(-6x^2-8x)=-(33x^2+41x)\)
4. \(8x^2-22x=6x^2-7x\)
5. \(-5(7x^2+7x)=-(40x^2+30x)\)
6. \(-4(-7x^2+3x)=-(-27x^2+7x)\)
7. \(6x^2+14x=0\)
8. \(-3x^2+8x=-4x^2+8x\)
9. \(4x^2-20x=0\)
10. \(-16x^2+14x=-9x^2-7x\)
11. \(-3(6x^2-5x)=-(13x^2-17x)\)
12. \(-6x^2+25x=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(8x^2+11x=0 \\ \Leftrightarrow x(8x+11) = 0 \\ \Leftrightarrow x = 0 \vee 8x+11=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-11}{8} \\ V = \Big\{ 0 ; \frac{-11}{8} \Big\} \\ -----------------\)
2. \(-4(-5x^2+7x)=-(-21x^2+52x) \\ \Leftrightarrow 20x^2-28x=21x^2-52x \\ \Leftrightarrow 20x^2-28x-21x^2+52x= 0 \\ \Leftrightarrow -x^2-24x=0 \\ \Leftrightarrow x(-x-24) = 0 \\ \Leftrightarrow x = 0 \vee -x-24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{24}{-1} = -24 \\ V = \Big\{ 0 ; -24 \Big\} \\ -----------------\)
3. \(5(-6x^2-8x)=-(33x^2+41x) \\ \Leftrightarrow -30x^2-40x=-33x^2-41x \\ \Leftrightarrow -30x^2-40x+33x^2+41x= 0 \\ \Leftrightarrow 3x^2-1x=0 \\ \Leftrightarrow x(3x-1) = 0 \\ \Leftrightarrow x = 0 \vee 3x-1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{1}{3} \\ V = \Big\{ \frac{1}{3}; 0 \Big\} \\ -----------------\)
4. \(8x^2-22x=6x^2-7x \\ \Leftrightarrow 2x^2-15x=0 \\ \Leftrightarrow x(2x-15) = 0 \\ \Leftrightarrow x = 0 \vee 2x-15=0 \\ \Leftrightarrow x = 0 \vee x = \frac{15}{2} \\ V = \Big\{ \frac{15}{2}; 0 \Big\} \\ -----------------\)
5. \(-5(7x^2+7x)=-(40x^2+30x) \\ \Leftrightarrow -35x^2-35x=-40x^2-30x \\ \Leftrightarrow -35x^2-35x+40x^2+30x= 0 \\ \Leftrightarrow 5x^2+5x=0 \\ \Leftrightarrow x(5x+5) = 0 \\ \Leftrightarrow x = 0 \vee 5x+5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-5}{5} = -1 \\ V = \Big\{ 0 ; -1 \Big\} \\ -----------------\)
6. \(-4(-7x^2+3x)=-(-27x^2+7x) \\ \Leftrightarrow 28x^2-12x=27x^2-7x \\ \Leftrightarrow 28x^2-12x-27x^2+7x= 0 \\ \Leftrightarrow x^2+5x=0 \\ \Leftrightarrow x(x+5) = 0 \\ \Leftrightarrow x = 0 \vee x+5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-5}{1} = -5 \\ V = \Big\{ 0 ; -5 \Big\} \\ -----------------\)
7. \(6x^2+14x=0 \\ \Leftrightarrow x(6x+14) = 0 \\ \Leftrightarrow x = 0 \vee 6x+14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-14}{6} = \frac{-7}{3} \\ V = \Big\{ 0 ; \frac{-7}{3} \Big\} \\ -----------------\)
8. \(-3x^2+8x=-4x^2+8x \\ \Leftrightarrow x^2+0x=0 \\ \Leftrightarrow x^2=0 \\ \Leftrightarrow x^2 = \frac{0}{1} \\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
9. \(4x^2-20x=0 \\ \Leftrightarrow x(4x-20) = 0 \\ \Leftrightarrow x = 0 \vee 4x-20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{20}{4} = 5 \\ V = \Big\{ 5; 0 \Big\} \\ -----------------\)
10. \(-16x^2+14x=-9x^2-7x \\ \Leftrightarrow -7x^2+21x=0 \\ \Leftrightarrow x(-7x+21) = 0 \\ \Leftrightarrow x = 0 \vee -7x+21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-21}{-7} = 3 \\ V = \Big\{ 3; 0 \Big\} \\ -----------------\)
11. \(-3(6x^2-5x)=-(13x^2-17x) \\ \Leftrightarrow -18x^2+15x=-13x^2+17x \\ \Leftrightarrow -18x^2+15x+13x^2-17x= 0 \\ \Leftrightarrow -5x^2+2x=0 \\ \Leftrightarrow x(-5x+2) = 0 \\ \Leftrightarrow x = 0 \vee -5x+2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-2}{-5} = \frac{2}{5} \\ V = \Big\{ \frac{2}{5}; 0 \Big\} \\ -----------------\)
12. \(-6x^2+25x=0 \\ \Leftrightarrow x(-6x+25) = 0 \\ \Leftrightarrow x = 0 \vee -6x+25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-25}{-6} = \frac{25}{6} \\ V = \Big\{ \frac{25}{6}; 0 \Big\} \\ -----------------\)