Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-3(-6x^2-2x)=-(-22x^2-22x)\)
2. \(-x^2+14x=0\)
3. \(x^2+18x=-3x^2-7x\)
4. \(-8x^2-9x=-9x^2+4x\)
5. \(-5(-3x^2+5x)=-(-22x^2+3x)\)
6. \(8x^2+5x=0\)
7. \(-8x^2+18x=-10x^2+10x\)
8. \(4x^2+19x=0\)
9. \(-3x^2-11x=0\)
10. \(3x^2+16x=-5x^2-4x\)
11. \(x^2-18x=0\)
12. \(-8x^2+25x=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-3(-6x^2-2x)=-(-22x^2-22x) \\ \Leftrightarrow 18x^2+6x=22x^2+22x \\ \Leftrightarrow 18x^2+6x-22x^2-22x= 0 \\ \Leftrightarrow -4x^2+16x=0 \\ \Leftrightarrow x(-4x+16) = 0 \\ \Leftrightarrow x = 0 \vee -4x+16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-16}{-4} = 4 \\ V = \Big\{ 4; 0 \Big\} \\ -----------------\)
2. \(-x^2+14x=0 \\ \Leftrightarrow x(-x+14) = 0 \\ \Leftrightarrow x = 0 \vee -x+14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-14}{-1} = 14 \\ V = \Big\{ 14; 0 \Big\} \\ -----------------\)
3. \(x^2+18x=-3x^2-7x \\ \Leftrightarrow 4x^2+25x=0 \\ \Leftrightarrow x(4x+25) = 0 \\ \Leftrightarrow x = 0 \vee 4x+25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-25}{4} \\ V = \Big\{ 0 ; \frac{-25}{4} \Big\} \\ -----------------\)
4. \(-8x^2-9x=-9x^2+4x \\ \Leftrightarrow x^2-13x=0 \\ \Leftrightarrow x(x-13) = 0 \\ \Leftrightarrow x = 0 \vee x-13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{13}{1} = 13 \\ V = \Big\{ 13; 0 \Big\} \\ -----------------\)
5. \(-5(-3x^2+5x)=-(-22x^2+3x) \\ \Leftrightarrow 15x^2-25x=22x^2-3x \\ \Leftrightarrow 15x^2-25x-22x^2+3x= 0 \\ \Leftrightarrow -7x^2+22x=0 \\ \Leftrightarrow x(-7x+22) = 0 \\ \Leftrightarrow x = 0 \vee -7x+22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-22}{-7} = \frac{22}{7} \\ V = \Big\{ \frac{22}{7}; 0 \Big\} \\ -----------------\)
6. \(8x^2+5x=0 \\ \Leftrightarrow x(8x+5) = 0 \\ \Leftrightarrow x = 0 \vee 8x+5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-5}{8} \\ V = \Big\{ 0 ; \frac{-5}{8} \Big\} \\ -----------------\)
7. \(-8x^2+18x=-10x^2+10x \\ \Leftrightarrow 2x^2+8x=0 \\ \Leftrightarrow x(2x+8) = 0 \\ \Leftrightarrow x = 0 \vee 2x+8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-8}{2} = -4 \\ V = \Big\{ 0 ; -4 \Big\} \\ -----------------\)
8. \(4x^2+19x=0 \\ \Leftrightarrow x(4x+19) = 0 \\ \Leftrightarrow x = 0 \vee 4x+19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-19}{4} \\ V = \Big\{ 0 ; \frac{-19}{4} \Big\} \\ -----------------\)
9. \(-3x^2-11x=0 \\ \Leftrightarrow x(-3x-11) = 0 \\ \Leftrightarrow x = 0 \vee -3x-11=0 \\ \Leftrightarrow x = 0 \vee x = \frac{11}{-3} = \frac{-11}{3} \\ V = \Big\{ 0 ; \frac{-11}{3} \Big\} \\ -----------------\)
10. \(3x^2+16x=-5x^2-4x \\ \Leftrightarrow 8x^2+20x=0 \\ \Leftrightarrow x(8x+20) = 0 \\ \Leftrightarrow x = 0 \vee 8x+20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-20}{8} = \frac{-5}{2} \\ V = \Big\{ 0 ; \frac{-5}{2} \Big\} \\ -----------------\)
11. \(x^2-18x=0 \\ \Leftrightarrow x(x-18) = 0 \\ \Leftrightarrow x = 0 \vee x-18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{18}{1} = 18 \\ V = \Big\{ 18; 0 \Big\} \\ -----------------\)
12. \(-8x^2+25x=0 \\ \Leftrightarrow x(-8x+25) = 0 \\ \Leftrightarrow x = 0 \vee -8x+25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-25}{-8} = \frac{25}{8} \\ V = \Big\{ \frac{25}{8}; 0 \Big\} \\ -----------------\)