Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-3x^2-22x=0\)
2. \(-8x^2+5x=0\)
3. \(2(-3x^2+6x)=-(12x^2+12x)\)
4. \(-3x^2-3x=0\)
5. \(-15x^2-7x=-7x^2-4x\)
6. \(4(-6x^2-5x)=-(17x^2+20x)\)
7. \(-14x^2+6x=-10x^2-4x\)
8. \(4(2x^2-6x)=-(-2x^2+39x)\)
9. \(3(5x^2+6x)=-(-18x^2-34x)\)
10. \(-7x^2+25x=0\)
11. \(-x^2-3x=0\)
12. \(-6x^2-25x=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-3x^2-22x=0 \\ \Leftrightarrow x(-3x-22) = 0 \\ \Leftrightarrow x = 0 \vee -3x-22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{22}{-3} = \frac{-22}{3} \\ V = \Big\{ 0 ; \frac{-22}{3} \Big\} \\ -----------------\)
2. \(-8x^2+5x=0 \\ \Leftrightarrow x(-8x+5) = 0 \\ \Leftrightarrow x = 0 \vee -8x+5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-5}{-8} = \frac{5}{8} \\ V = \Big\{ \frac{5}{8}; 0 \Big\} \\ -----------------\)
3. \(2(-3x^2+6x)=-(12x^2+12x) \\ \Leftrightarrow -6x^2+12x=-12x^2-12x \\ \Leftrightarrow -6x^2+12x+12x^2+12x= 0 \\ \Leftrightarrow 6x^2-24x=0 \\ \Leftrightarrow x(6x-24) = 0 \\ \Leftrightarrow x = 0 \vee 6x-24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{24}{6} = 4 \\ V = \Big\{ 4; 0 \Big\} \\ -----------------\)
4. \(-3x^2-3x=0 \\ \Leftrightarrow x(-3x-3) = 0 \\ \Leftrightarrow x = 0 \vee -3x-3=0 \\ \Leftrightarrow x = 0 \vee x = \frac{3}{-3} = -1 \\ V = \Big\{ 0 ; -1 \Big\} \\ -----------------\)
5. \(-15x^2-7x=-7x^2-4x \\ \Leftrightarrow -8x^2-3x=0 \\ \Leftrightarrow x(-8x-3) = 0 \\ \Leftrightarrow x = 0 \vee -8x-3=0 \\ \Leftrightarrow x = 0 \vee x = \frac{3}{-8} = \frac{-3}{8} \\ V = \Big\{ 0 ; \frac{-3}{8} \Big\} \\ -----------------\)
6. \(4(-6x^2-5x)=-(17x^2+20x) \\ \Leftrightarrow -24x^2-20x=-17x^2-20x \\ \Leftrightarrow -24x^2-20x+17x^2+20x= 0 \\ \Leftrightarrow -7x^2+0x=0 \\ \Leftrightarrow -7x^2=0 \\ \Leftrightarrow x^2 = \frac{0}{-7} \\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
7. \(-14x^2+6x=-10x^2-4x \\ \Leftrightarrow -4x^2+10x=0 \\ \Leftrightarrow x(-4x+10) = 0 \\ \Leftrightarrow x = 0 \vee -4x+10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-10}{-4} = \frac{5}{2} \\ V = \Big\{ \frac{5}{2}; 0 \Big\} \\ -----------------\)
8. \(4(2x^2-6x)=-(-2x^2+39x) \\ \Leftrightarrow 8x^2-24x=2x^2-39x \\ \Leftrightarrow 8x^2-24x-2x^2+39x= 0 \\ \Leftrightarrow 6x^2-15x=0 \\ \Leftrightarrow x(6x-15) = 0 \\ \Leftrightarrow x = 0 \vee 6x-15=0 \\ \Leftrightarrow x = 0 \vee x = \frac{15}{6} = \frac{5}{2} \\ V = \Big\{ \frac{5}{2}; 0 \Big\} \\ -----------------\)
9. \(3(5x^2+6x)=-(-18x^2-34x) \\ \Leftrightarrow 15x^2+18x=18x^2+34x \\ \Leftrightarrow 15x^2+18x-18x^2-34x= 0 \\ \Leftrightarrow -3x^2+16x=0 \\ \Leftrightarrow x(-3x+16) = 0 \\ \Leftrightarrow x = 0 \vee -3x+16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-16}{-3} = \frac{16}{3} \\ V = \Big\{ \frac{16}{3}; 0 \Big\} \\ -----------------\)
10. \(-7x^2+25x=0 \\ \Leftrightarrow x(-7x+25) = 0 \\ \Leftrightarrow x = 0 \vee -7x+25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-25}{-7} = \frac{25}{7} \\ V = \Big\{ \frac{25}{7}; 0 \Big\} \\ -----------------\)
11. \(-x^2-3x=0 \\ \Leftrightarrow x(-x-3) = 0 \\ \Leftrightarrow x = 0 \vee -x-3=0 \\ \Leftrightarrow x = 0 \vee x = \frac{3}{-1} = -3 \\ V = \Big\{ 0 ; -3 \Big\} \\ -----------------\)
12. \(-6x^2-25x=0 \\ \Leftrightarrow x(-6x-25) = 0 \\ \Leftrightarrow x = 0 \vee -6x-25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{25}{-6} = \frac{-25}{6} \\ V = \Big\{ 0 ; \frac{-25}{6} \Big\} \\ -----------------\)