Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(2(3x^2+3x)=-(2x^2+8x)\)
2. \(-11x^2+3x=-7x^2-8x\)
3. \(8x^2-33x=3x^2-9x\)
4. \(4x^2-22x=0\)
5. \(-2(-3x^2-6x)=-(-8x^2+4x)\)
6. \(2x^2+18x=0\)
7. \(-3(2x^2-8x)=-(-2x^2-17x)\)
8. \(12x^2+x=7x^2+5x\)
9. \(x^2-6x=0\)
10. \(-5(-9x^2+9x)=-(-49x^2+28x)\)
11. \(-3x^2-10x=0\)
12. \(4(-8x^2-10x)=-(30x^2+39x)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(2(3x^2+3x)=-(2x^2+8x) \\ \Leftrightarrow 6x^2+6x=-2x^2-8x \\ \Leftrightarrow 6x^2+6x+2x^2+8x= 0 \\ \Leftrightarrow 8x^2-14x=0 \\ \Leftrightarrow x(8x-14) = 0 \\ \Leftrightarrow x = 0 \vee 8x-14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{14}{8} = \frac{7}{4} \\ V = \Big\{ \frac{7}{4}; 0 \Big\} \\ -----------------\)
2. \(-11x^2+3x=-7x^2-8x \\ \Leftrightarrow -4x^2+11x=0 \\ \Leftrightarrow x(-4x+11) = 0 \\ \Leftrightarrow x = 0 \vee -4x+11=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-11}{-4} = \frac{11}{4} \\ V = \Big\{ \frac{11}{4}; 0 \Big\} \\ -----------------\)
3. \(8x^2-33x=3x^2-9x \\ \Leftrightarrow 5x^2-24x=0 \\ \Leftrightarrow x(5x-24) = 0 \\ \Leftrightarrow x = 0 \vee 5x-24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{24}{5} \\ V = \Big\{ \frac{24}{5}; 0 \Big\} \\ -----------------\)
4. \(4x^2-22x=0 \\ \Leftrightarrow x(4x-22) = 0 \\ \Leftrightarrow x = 0 \vee 4x-22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{22}{4} = \frac{11}{2} \\ V = \Big\{ \frac{11}{2}; 0 \Big\} \\ -----------------\)
5. \(-2(-3x^2-6x)=-(-8x^2+4x) \\ \Leftrightarrow 6x^2+12x=8x^2-4x \\ \Leftrightarrow 6x^2+12x-8x^2+4x= 0 \\ \Leftrightarrow -2x^2-16x=0 \\ \Leftrightarrow x(-2x-16) = 0 \\ \Leftrightarrow x = 0 \vee -2x-16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{16}{-2} = -8 \\ V = \Big\{ 0 ; -8 \Big\} \\ -----------------\)
6. \(2x^2+18x=0 \\ \Leftrightarrow x(2x+18) = 0 \\ \Leftrightarrow x = 0 \vee 2x+18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-18}{2} = -9 \\ V = \Big\{ 0 ; -9 \Big\} \\ -----------------\)
7. \(-3(2x^2-8x)=-(-2x^2-17x) \\ \Leftrightarrow -6x^2+24x=2x^2+17x \\ \Leftrightarrow -6x^2+24x-2x^2-17x= 0 \\ \Leftrightarrow -8x^2-7x=0 \\ \Leftrightarrow x(-8x-7) = 0 \\ \Leftrightarrow x = 0 \vee -8x-7=0 \\ \Leftrightarrow x = 0 \vee x = \frac{7}{-8} = \frac{-7}{8} \\ V = \Big\{ 0 ; \frac{-7}{8} \Big\} \\ -----------------\)
8. \(12x^2+x=7x^2+5x \\ \Leftrightarrow 5x^2-4x=0 \\ \Leftrightarrow x(5x-4) = 0 \\ \Leftrightarrow x = 0 \vee 5x-4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{4}{5} \\ V = \Big\{ \frac{4}{5}; 0 \Big\} \\ -----------------\)
9. \(x^2-6x=0 \\ \Leftrightarrow x(x-6) = 0 \\ \Leftrightarrow x = 0 \vee x-6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{6}{1} = 6 \\ V = \Big\{ 6; 0 \Big\} \\ -----------------\)
10. \(-5(-9x^2+9x)=-(-49x^2+28x) \\ \Leftrightarrow 45x^2-45x=49x^2-28x \\ \Leftrightarrow 45x^2-45x-49x^2+28x= 0 \\ \Leftrightarrow -4x^2+17x=0 \\ \Leftrightarrow x(-4x+17) = 0 \\ \Leftrightarrow x = 0 \vee -4x+17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-17}{-4} = \frac{17}{4} \\ V = \Big\{ \frac{17}{4}; 0 \Big\} \\ -----------------\)
11. \(-3x^2-10x=0 \\ \Leftrightarrow x(-3x-10) = 0 \\ \Leftrightarrow x = 0 \vee -3x-10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{10}{-3} = \frac{-10}{3} \\ V = \Big\{ 0 ; \frac{-10}{3} \Big\} \\ -----------------\)
12. \(4(-8x^2-10x)=-(30x^2+39x) \\ \Leftrightarrow -32x^2-40x=-30x^2-39x \\ \Leftrightarrow -32x^2-40x+30x^2+39x= 0 \\ \Leftrightarrow -2x^2+1x=0 \\ \Leftrightarrow x(-2x+1) = 0 \\ \Leftrightarrow x = 0 \vee -2x+1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-1}{-2} = \frac{1}{2} \\ V = \Big\{ \frac{1}{2}; 0 \Big\} \\ -----------------\)