Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-8x^2-5x=0\)
2. \(-2x^2-5x=5x^2-9x\)
3. \(4(10x^2+10x)=-(-34x^2-47x)\)
4. \(-x^2+9x=0\)
5. \(5(-3x^2-3x)=-(22x^2-2x)\)
6. \(-9x^2-x=-5x^2+6x\)
7. \(5(10x^2-6x)=-(-42x^2+10x)\)
8. \(2(-5x^2-3x)=-(11x^2+16x)\)
9. \(-x^2+27x=2x^2+2x\)
10. \(12x^2-7x=4x^2+7x\)
11. \(-3(5x^2+9x)=-(8x^2+13x)\)
12. \(-5x^2+8x=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-8x^2-5x=0 \\ \Leftrightarrow x(-8x-5) = 0 \\ \Leftrightarrow x = 0 \vee -8x-5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{5}{-8} = \frac{-5}{8} \\ V = \Big\{ 0 ; \frac{-5}{8} \Big\} \\ -----------------\)
2. \(-2x^2-5x=5x^2-9x \\ \Leftrightarrow -7x^2+4x=0 \\ \Leftrightarrow x(-7x+4) = 0 \\ \Leftrightarrow x = 0 \vee -7x+4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-4}{-7} = \frac{4}{7} \\ V = \Big\{ \frac{4}{7}; 0 \Big\} \\ -----------------\)
3. \(4(10x^2+10x)=-(-34x^2-47x) \\ \Leftrightarrow 40x^2+40x=34x^2+47x \\ \Leftrightarrow 40x^2+40x-34x^2-47x= 0 \\ \Leftrightarrow 6x^2+7x=0 \\ \Leftrightarrow x(6x+7) = 0 \\ \Leftrightarrow x = 0 \vee 6x+7=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-7}{6} \\ V = \Big\{ 0 ; \frac{-7}{6} \Big\} \\ -----------------\)
4. \(-x^2+9x=0 \\ \Leftrightarrow x(-x+9) = 0 \\ \Leftrightarrow x = 0 \vee -x+9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-9}{-1} = 9 \\ V = \Big\{ 9; 0 \Big\} \\ -----------------\)
5. \(5(-3x^2-3x)=-(22x^2-2x) \\ \Leftrightarrow -15x^2-15x=-22x^2+2x \\ \Leftrightarrow -15x^2-15x+22x^2-2x= 0 \\ \Leftrightarrow 7x^2+17x=0 \\ \Leftrightarrow x(7x+17) = 0 \\ \Leftrightarrow x = 0 \vee 7x+17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-17}{7} \\ V = \Big\{ 0 ; \frac{-17}{7} \Big\} \\ -----------------\)
6. \(-9x^2-x=-5x^2+6x \\ \Leftrightarrow -4x^2-7x=0 \\ \Leftrightarrow x(-4x-7) = 0 \\ \Leftrightarrow x = 0 \vee -4x-7=0 \\ \Leftrightarrow x = 0 \vee x = \frac{7}{-4} = \frac{-7}{4} \\ V = \Big\{ 0 ; \frac{-7}{4} \Big\} \\ -----------------\)
7. \(5(10x^2-6x)=-(-42x^2+10x) \\ \Leftrightarrow 50x^2-30x=42x^2-10x \\ \Leftrightarrow 50x^2-30x-42x^2+10x= 0 \\ \Leftrightarrow 8x^2+20x=0 \\ \Leftrightarrow x(8x+20) = 0 \\ \Leftrightarrow x = 0 \vee 8x+20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-20}{8} = \frac{-5}{2} \\ V = \Big\{ 0 ; \frac{-5}{2} \Big\} \\ -----------------\)
8. \(2(-5x^2-3x)=-(11x^2+16x) \\ \Leftrightarrow -10x^2-6x=-11x^2-16x \\ \Leftrightarrow -10x^2-6x+11x^2+16x= 0 \\ \Leftrightarrow x^2-10x=0 \\ \Leftrightarrow x(x-10) = 0 \\ \Leftrightarrow x = 0 \vee x-10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{10}{1} = 10 \\ V = \Big\{ 10; 0 \Big\} \\ -----------------\)
9. \(-x^2+27x=2x^2+2x \\ \Leftrightarrow -3x^2+25x=0 \\ \Leftrightarrow x(-3x+25) = 0 \\ \Leftrightarrow x = 0 \vee -3x+25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-25}{-3} = \frac{25}{3} \\ V = \Big\{ \frac{25}{3}; 0 \Big\} \\ -----------------\)
10. \(12x^2-7x=4x^2+7x \\ \Leftrightarrow 8x^2-14x=0 \\ \Leftrightarrow x(8x-14) = 0 \\ \Leftrightarrow x = 0 \vee 8x-14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{14}{8} = \frac{7}{4} \\ V = \Big\{ \frac{7}{4}; 0 \Big\} \\ -----------------\)
11. \(-3(5x^2+9x)=-(8x^2+13x) \\ \Leftrightarrow -15x^2-27x=-8x^2-13x \\ \Leftrightarrow -15x^2-27x+8x^2+13x= 0 \\ \Leftrightarrow -7x^2+14x=0 \\ \Leftrightarrow x(-7x+14) = 0 \\ \Leftrightarrow x = 0 \vee -7x+14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-14}{-7} = 2 \\ V = \Big\{ 2; 0 \Big\} \\ -----------------\)
12. \(-5x^2+8x=0 \\ \Leftrightarrow x(-5x+8) = 0 \\ \Leftrightarrow x = 0 \vee -5x+8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-8}{-5} = \frac{8}{5} \\ V = \Big\{ \frac{8}{5}; 0 \Big\} \\ -----------------\)