Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-8x^2+22x=-9x^2+4x\)
2. \(-4x^2-9x=-10x^2-7x\)
3. \(4(-3x^2+5x)=-(6x^2-28x)\)
4. \(2x^2+9x=-2x^2-8x\)
5. \(15x^2-7x=10x^2-2x\)
6. \(-8x^2+9x=-5x^2-2x\)
7. \(-x^2+23x=0\)
8. \(5x^2-20x=2x^2+4x\)
9. \(3(-4x^2+7x)=-(13x^2+3x)\)
10. \(-3(4x^2-4x)=-(18x^2-19x)\)
11. \(-5(-5x^2-3x)=-(-24x^2-21x)\)
12. \(-7x^2+9x=-4x^2-8x\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-8x^2+22x=-9x^2+4x \\ \Leftrightarrow x^2+18x=0 \\ \Leftrightarrow x(x+18) = 0 \\ \Leftrightarrow x = 0 \vee x+18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-18}{1} = -18 \\ V = \Big\{ 0 ; -18 \Big\} \\ -----------------\)
2. \(-4x^2-9x=-10x^2-7x \\ \Leftrightarrow 6x^2-2x=0 \\ \Leftrightarrow x(6x-2) = 0 \\ \Leftrightarrow x = 0 \vee 6x-2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{2}{6} = \frac{1}{3} \\ V = \Big\{ \frac{1}{3}; 0 \Big\} \\ -----------------\)
3. \(4(-3x^2+5x)=-(6x^2-28x) \\ \Leftrightarrow -12x^2+20x=-6x^2+28x \\ \Leftrightarrow -12x^2+20x+6x^2-28x= 0 \\ \Leftrightarrow -6x^2+8x=0 \\ \Leftrightarrow x(-6x+8) = 0 \\ \Leftrightarrow x = 0 \vee -6x+8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-8}{-6} = \frac{4}{3} \\ V = \Big\{ \frac{4}{3}; 0 \Big\} \\ -----------------\)
4. \(2x^2+9x=-2x^2-8x \\ \Leftrightarrow 4x^2+17x=0 \\ \Leftrightarrow x(4x+17) = 0 \\ \Leftrightarrow x = 0 \vee 4x+17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-17}{4} \\ V = \Big\{ 0 ; \frac{-17}{4} \Big\} \\ -----------------\)
5. \(15x^2-7x=10x^2-2x \\ \Leftrightarrow 5x^2-5x=0 \\ \Leftrightarrow x(5x-5) = 0 \\ \Leftrightarrow x = 0 \vee 5x-5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{5}{5} = 1 \\ V = \Big\{ 1; 0 \Big\} \\ -----------------\)
6. \(-8x^2+9x=-5x^2-2x \\ \Leftrightarrow -3x^2+11x=0 \\ \Leftrightarrow x(-3x+11) = 0 \\ \Leftrightarrow x = 0 \vee -3x+11=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-11}{-3} = \frac{11}{3} \\ V = \Big\{ \frac{11}{3}; 0 \Big\} \\ -----------------\)
7. \(-x^2+23x=0 \\ \Leftrightarrow x(-x+23) = 0 \\ \Leftrightarrow x = 0 \vee -x+23=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-23}{-1} = 23 \\ V = \Big\{ 23; 0 \Big\} \\ -----------------\)
8. \(5x^2-20x=2x^2+4x \\ \Leftrightarrow 3x^2-24x=0 \\ \Leftrightarrow x(3x-24) = 0 \\ \Leftrightarrow x = 0 \vee 3x-24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{24}{3} = 8 \\ V = \Big\{ 8; 0 \Big\} \\ -----------------\)
9. \(3(-4x^2+7x)=-(13x^2+3x) \\ \Leftrightarrow -12x^2+21x=-13x^2-3x \\ \Leftrightarrow -12x^2+21x+13x^2+3x= 0 \\ \Leftrightarrow x^2-24x=0 \\ \Leftrightarrow x(x-24) = 0 \\ \Leftrightarrow x = 0 \vee x-24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{24}{1} = 24 \\ V = \Big\{ 24; 0 \Big\} \\ -----------------\)
10. \(-3(4x^2-4x)=-(18x^2-19x) \\ \Leftrightarrow -12x^2+12x=-18x^2+19x \\ \Leftrightarrow -12x^2+12x+18x^2-19x= 0 \\ \Leftrightarrow 6x^2+7x=0 \\ \Leftrightarrow x(6x+7) = 0 \\ \Leftrightarrow x = 0 \vee 6x+7=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-7}{6} \\ V = \Big\{ 0 ; \frac{-7}{6} \Big\} \\ -----------------\)
11. \(-5(-5x^2-3x)=-(-24x^2-21x) \\ \Leftrightarrow 25x^2+15x=24x^2+21x \\ \Leftrightarrow 25x^2+15x-24x^2-21x= 0 \\ \Leftrightarrow x^2+6x=0 \\ \Leftrightarrow x(x+6) = 0 \\ \Leftrightarrow x = 0 \vee x+6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-6}{1} = -6 \\ V = \Big\{ 0 ; -6 \Big\} \\ -----------------\)
12. \(-7x^2+9x=-4x^2-8x \\ \Leftrightarrow -3x^2+17x=0 \\ \Leftrightarrow x(-3x+17) = 0 \\ \Leftrightarrow x = 0 \vee -3x+17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-17}{-3} = \frac{17}{3} \\ V = \Big\{ \frac{17}{3}; 0 \Big\} \\ -----------------\)