Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(7x^2+14x=0\)
2. \(-5(8x^2-4x)=-(47x^2-42x)\)
3. \(-3x^2+5x=5x^2-2x\)
4. \(-15x^2+4x=-9x^2-10x\)
5. \(-3(4x^2-10x)=-(10x^2-10x)\)
6. \(2x^2-25x=0\)
7. \(-2(-2x^2-2x)=-(-8x^2+13x)\)
8. \(4x^2-6x=0\)
9. \(-7x^2-24x=0\)
10. \(-3x^2+2x=-5x^2+5x\)
11. \(6x^2-12x=-2x^2+8x\)
12. \(-2x^2-x=-7x^2+3x\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(7x^2+14x=0 \\ \Leftrightarrow x(7x+14) = 0 \\ \Leftrightarrow x = 0 \vee 7x+14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-14}{7} = -2 \\ V = \Big\{ 0 ; -2 \Big\} \\ -----------------\)
2. \(-5(8x^2-4x)=-(47x^2-42x) \\ \Leftrightarrow -40x^2+20x=-47x^2+42x \\ \Leftrightarrow -40x^2+20x+47x^2-42x= 0 \\ \Leftrightarrow 7x^2+22x=0 \\ \Leftrightarrow x(7x+22) = 0 \\ \Leftrightarrow x = 0 \vee 7x+22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-22}{7} \\ V = \Big\{ 0 ; \frac{-22}{7} \Big\} \\ -----------------\)
3. \(-3x^2+5x=5x^2-2x \\ \Leftrightarrow -8x^2+7x=0 \\ \Leftrightarrow x(-8x+7) = 0 \\ \Leftrightarrow x = 0 \vee -8x+7=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-7}{-8} = \frac{7}{8} \\ V = \Big\{ \frac{7}{8}; 0 \Big\} \\ -----------------\)
4. \(-15x^2+4x=-9x^2-10x \\ \Leftrightarrow -6x^2+14x=0 \\ \Leftrightarrow x(-6x+14) = 0 \\ \Leftrightarrow x = 0 \vee -6x+14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-14}{-6} = \frac{7}{3} \\ V = \Big\{ \frac{7}{3}; 0 \Big\} \\ -----------------\)
5. \(-3(4x^2-10x)=-(10x^2-10x) \\ \Leftrightarrow -12x^2+30x=-10x^2+10x \\ \Leftrightarrow -12x^2+30x+10x^2-10x= 0 \\ \Leftrightarrow -2x^2-20x=0 \\ \Leftrightarrow x(-2x-20) = 0 \\ \Leftrightarrow x = 0 \vee -2x-20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{20}{-2} = -10 \\ V = \Big\{ 0 ; -10 \Big\} \\ -----------------\)
6. \(2x^2-25x=0 \\ \Leftrightarrow x(2x-25) = 0 \\ \Leftrightarrow x = 0 \vee 2x-25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{25}{2} \\ V = \Big\{ \frac{25}{2}; 0 \Big\} \\ -----------------\)
7. \(-2(-2x^2-2x)=-(-8x^2+13x) \\ \Leftrightarrow 4x^2+4x=8x^2-13x \\ \Leftrightarrow 4x^2+4x-8x^2+13x= 0 \\ \Leftrightarrow -4x^2-17x=0 \\ \Leftrightarrow x(-4x-17) = 0 \\ \Leftrightarrow x = 0 \vee -4x-17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{17}{-4} = \frac{-17}{4} \\ V = \Big\{ 0 ; \frac{-17}{4} \Big\} \\ -----------------\)
8. \(4x^2-6x=0 \\ \Leftrightarrow x(4x-6) = 0 \\ \Leftrightarrow x = 0 \vee 4x-6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{6}{4} = \frac{3}{2} \\ V = \Big\{ \frac{3}{2}; 0 \Big\} \\ -----------------\)
9. \(-7x^2-24x=0 \\ \Leftrightarrow x(-7x-24) = 0 \\ \Leftrightarrow x = 0 \vee -7x-24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{24}{-7} = \frac{-24}{7} \\ V = \Big\{ 0 ; \frac{-24}{7} \Big\} \\ -----------------\)
10. \(-3x^2+2x=-5x^2+5x \\ \Leftrightarrow 2x^2-3x=0 \\ \Leftrightarrow x(2x-3) = 0 \\ \Leftrightarrow x = 0 \vee 2x-3=0 \\ \Leftrightarrow x = 0 \vee x = \frac{3}{2} \\ V = \Big\{ \frac{3}{2}; 0 \Big\} \\ -----------------\)
11. \(6x^2-12x=-2x^2+8x \\ \Leftrightarrow 8x^2-20x=0 \\ \Leftrightarrow x(8x-20) = 0 \\ \Leftrightarrow x = 0 \vee 8x-20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{20}{8} = \frac{5}{2} \\ V = \Big\{ \frac{5}{2}; 0 \Big\} \\ -----------------\)
12. \(-2x^2-x=-7x^2+3x \\ \Leftrightarrow 5x^2-4x=0 \\ \Leftrightarrow x(5x-4) = 0 \\ \Leftrightarrow x = 0 \vee 5x-4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{4}{5} \\ V = \Big\{ \frac{4}{5}; 0 \Big\} \\ -----------------\)