Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-6x^2+15x=-8x^2-3x\)
2. \(-3(8x^2+6x)=-(30x^2+25x)\)
3. \(-4(7x^2+9x)=-(36x^2+32x)\)
4. \(2x^2+13x=0\)
5. \(-5(-7x^2-2x)=-(-38x^2-28x)\)
6. \(-2(3x^2-5x)=-(x^2-10x)\)
7. \(5(-8x^2+7x)=-(36x^2-21x)\)
8. \(8x^2+24x=0\)
9. \(3x^2+11x=9x^2+9x\)
10. \(-8x^2-15x=-9x^2-2x\)
11. \(-3(6x^2+10x)=-(11x^2+44x)\)
12. \(-x^2-14x=6x^2+3x\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-6x^2+15x=-8x^2-3x \\ \Leftrightarrow 2x^2+18x=0 \\ \Leftrightarrow x(2x+18) = 0 \\ \Leftrightarrow x = 0 \vee 2x+18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-18}{2} = -9 \\ V = \Big\{ 0 ; -9 \Big\} \\ -----------------\)
2. \(-3(8x^2+6x)=-(30x^2+25x) \\ \Leftrightarrow -24x^2-18x=-30x^2-25x \\ \Leftrightarrow -24x^2-18x+30x^2+25x= 0 \\ \Leftrightarrow 6x^2-7x=0 \\ \Leftrightarrow x(6x-7) = 0 \\ \Leftrightarrow x = 0 \vee 6x-7=0 \\ \Leftrightarrow x = 0 \vee x = \frac{7}{6} \\ V = \Big\{ \frac{7}{6}; 0 \Big\} \\ -----------------\)
3. \(-4(7x^2+9x)=-(36x^2+32x) \\ \Leftrightarrow -28x^2-36x=-36x^2-32x \\ \Leftrightarrow -28x^2-36x+36x^2+32x= 0 \\ \Leftrightarrow 8x^2+4x=0 \\ \Leftrightarrow x(8x+4) = 0 \\ \Leftrightarrow x = 0 \vee 8x+4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-4}{8} = \frac{-1}{2} \\ V = \Big\{ 0 ; \frac{-1}{2} \Big\} \\ -----------------\)
4. \(2x^2+13x=0 \\ \Leftrightarrow x(2x+13) = 0 \\ \Leftrightarrow x = 0 \vee 2x+13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-13}{2} \\ V = \Big\{ 0 ; \frac{-13}{2} \Big\} \\ -----------------\)
5. \(-5(-7x^2-2x)=-(-38x^2-28x) \\ \Leftrightarrow 35x^2+10x=38x^2+28x \\ \Leftrightarrow 35x^2+10x-38x^2-28x= 0 \\ \Leftrightarrow -3x^2+18x=0 \\ \Leftrightarrow x(-3x+18) = 0 \\ \Leftrightarrow x = 0 \vee -3x+18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-18}{-3} = 6 \\ V = \Big\{ 6; 0 \Big\} \\ -----------------\)
6. \(-2(3x^2-5x)=-(x^2-10x) \\ \Leftrightarrow -6x^2+10x=-x^2+10x \\ \Leftrightarrow -6x^2+10x+x^2-10x= 0 \\ \Leftrightarrow -5x^2+0x=0 \\ \Leftrightarrow -5x^2=0 \\ \Leftrightarrow x^2 = \frac{0}{-5} \\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
7. \(5(-8x^2+7x)=-(36x^2-21x) \\ \Leftrightarrow -40x^2+35x=-36x^2+21x \\ \Leftrightarrow -40x^2+35x+36x^2-21x= 0 \\ \Leftrightarrow -4x^2-14x=0 \\ \Leftrightarrow x(-4x-14) = 0 \\ \Leftrightarrow x = 0 \vee -4x-14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{14}{-4} = \frac{-7}{2} \\ V = \Big\{ 0 ; \frac{-7}{2} \Big\} \\ -----------------\)
8. \(8x^2+24x=0 \\ \Leftrightarrow x(8x+24) = 0 \\ \Leftrightarrow x = 0 \vee 8x+24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-24}{8} = -3 \\ V = \Big\{ 0 ; -3 \Big\} \\ -----------------\)
9. \(3x^2+11x=9x^2+9x \\ \Leftrightarrow -6x^2+2x=0 \\ \Leftrightarrow x(-6x+2) = 0 \\ \Leftrightarrow x = 0 \vee -6x+2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-2}{-6} = \frac{1}{3} \\ V = \Big\{ \frac{1}{3}; 0 \Big\} \\ -----------------\)
10. \(-8x^2-15x=-9x^2-2x \\ \Leftrightarrow x^2-13x=0 \\ \Leftrightarrow x(x-13) = 0 \\ \Leftrightarrow x = 0 \vee x-13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{13}{1} = 13 \\ V = \Big\{ 13; 0 \Big\} \\ -----------------\)
11. \(-3(6x^2+10x)=-(11x^2+44x) \\ \Leftrightarrow -18x^2-30x=-11x^2-44x \\ \Leftrightarrow -18x^2-30x+11x^2+44x= 0 \\ \Leftrightarrow -7x^2-14x=0 \\ \Leftrightarrow x(-7x-14) = 0 \\ \Leftrightarrow x = 0 \vee -7x-14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{14}{-7} = -2 \\ V = \Big\{ 0 ; -2 \Big\} \\ -----------------\)
12. \(-x^2-14x=6x^2+3x \\ \Leftrightarrow -7x^2-17x=0 \\ \Leftrightarrow x(-7x-17) = 0 \\ \Leftrightarrow x = 0 \vee -7x-17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{17}{-7} = \frac{-17}{7} \\ V = \Big\{ 0 ; \frac{-17}{7} \Big\} \\ -----------------\)