Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-14x^2-33x=-9x^2-10x\)
2. \(-4x^2-13x=0\)
3. \(2x^2-20x=0\)
4. \(6x^2+13x=0\)
5. \(4x^2+19x=0\)
6. \(-8x^2+3x=-9x^2+9x\)
7. \(-2x^2+11x=0\)
8. \(5(-4x^2-5x)=-(25x^2+22x)\)
9. \(2(-9x^2+6x)=-(26x^2+9x)\)
10. \(-6x^2-9x=-7x^2-8x\)
11. \(3x^2+9x=10x^2-9x\)
12. \(-14x^2+3x=-6x^2+3x\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-14x^2-33x=-9x^2-10x \\ \Leftrightarrow -5x^2-23x=0 \\ \Leftrightarrow x(-5x-23) = 0 \\ \Leftrightarrow x = 0 \vee -5x-23=0 \\ \Leftrightarrow x = 0 \vee x = \frac{23}{-5} = \frac{-23}{5} \\ V = \Big\{ 0 ; \frac{-23}{5} \Big\} \\ -----------------\)
2. \(-4x^2-13x=0 \\ \Leftrightarrow x(-4x-13) = 0 \\ \Leftrightarrow x = 0 \vee -4x-13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{13}{-4} = \frac{-13}{4} \\ V = \Big\{ 0 ; \frac{-13}{4} \Big\} \\ -----------------\)
3. \(2x^2-20x=0 \\ \Leftrightarrow x(2x-20) = 0 \\ \Leftrightarrow x = 0 \vee 2x-20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{20}{2} = 10 \\ V = \Big\{ 10; 0 \Big\} \\ -----------------\)
4. \(6x^2+13x=0 \\ \Leftrightarrow x(6x+13) = 0 \\ \Leftrightarrow x = 0 \vee 6x+13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-13}{6} \\ V = \Big\{ 0 ; \frac{-13}{6} \Big\} \\ -----------------\)
5. \(4x^2+19x=0 \\ \Leftrightarrow x(4x+19) = 0 \\ \Leftrightarrow x = 0 \vee 4x+19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-19}{4} \\ V = \Big\{ 0 ; \frac{-19}{4} \Big\} \\ -----------------\)
6. \(-8x^2+3x=-9x^2+9x \\ \Leftrightarrow x^2-6x=0 \\ \Leftrightarrow x(x-6) = 0 \\ \Leftrightarrow x = 0 \vee x-6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{6}{1} = 6 \\ V = \Big\{ 6; 0 \Big\} \\ -----------------\)
7. \(-2x^2+11x=0 \\ \Leftrightarrow x(-2x+11) = 0 \\ \Leftrightarrow x = 0 \vee -2x+11=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-11}{-2} = \frac{11}{2} \\ V = \Big\{ \frac{11}{2}; 0 \Big\} \\ -----------------\)
8. \(5(-4x^2-5x)=-(25x^2+22x) \\ \Leftrightarrow -20x^2-25x=-25x^2-22x \\ \Leftrightarrow -20x^2-25x+25x^2+22x= 0 \\ \Leftrightarrow 5x^2+3x=0 \\ \Leftrightarrow x(5x+3) = 0 \\ \Leftrightarrow x = 0 \vee 5x+3=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-3}{5} \\ V = \Big\{ 0 ; \frac{-3}{5} \Big\} \\ -----------------\)
9. \(2(-9x^2+6x)=-(26x^2+9x) \\ \Leftrightarrow -18x^2+12x=-26x^2-9x \\ \Leftrightarrow -18x^2+12x+26x^2+9x= 0 \\ \Leftrightarrow 8x^2-21x=0 \\ \Leftrightarrow x(8x-21) = 0 \\ \Leftrightarrow x = 0 \vee 8x-21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{21}{8} \\ V = \Big\{ \frac{21}{8}; 0 \Big\} \\ -----------------\)
10. \(-6x^2-9x=-7x^2-8x \\ \Leftrightarrow x^2-1x=0 \\ \Leftrightarrow x(x-1) = 0 \\ \Leftrightarrow x = 0 \vee x-1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{1}{1} = 1 \\ V = \Big\{ 1; 0 \Big\} \\ -----------------\)
11. \(3x^2+9x=10x^2-9x \\ \Leftrightarrow -7x^2+18x=0 \\ \Leftrightarrow x(-7x+18) = 0 \\ \Leftrightarrow x = 0 \vee -7x+18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-18}{-7} = \frac{18}{7} \\ V = \Big\{ \frac{18}{7}; 0 \Big\} \\ -----------------\)
12. \(-14x^2+3x=-6x^2+3x \\ \Leftrightarrow -8x^2+0x=0 \\ \Leftrightarrow -8x^2=0 \\ \Leftrightarrow x^2 = \frac{0}{-8} \\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)