Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(5(-7x^2+5x)=-(38x^2-44x)\)
2. \(x^2-24x=-4x^2-7x\)
3. \(-2x^2-12x=5x^2+4x\)
4. \(4x^2+17x=0\)
5. \(3(9x^2-7x)=-(-33x^2+2x)\)
6. \(5(9x^2-4x)=-(-44x^2+28x)\)
7. \(-3(-10x^2-9x)=-(-35x^2-50x)\)
8. \(-x^2-33x=-8x^2-9x\)
9. \(-15x^2+31x=-9x^2+10x\)
10. \(3x^2-6x=0\)
11. \(4(-4x^2-2x)=-(11x^2+5x)\)
12. \(-x^2-10x=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(5(-7x^2+5x)=-(38x^2-44x) \\ \Leftrightarrow -35x^2+25x=-38x^2+44x \\ \Leftrightarrow -35x^2+25x+38x^2-44x= 0 \\ \Leftrightarrow 3x^2+19x=0 \\ \Leftrightarrow x(3x+19) = 0 \\ \Leftrightarrow x = 0 \vee 3x+19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-19}{3} \\ V = \Big\{ 0 ; \frac{-19}{3} \Big\} \\ -----------------\)
2. \(x^2-24x=-4x^2-7x \\ \Leftrightarrow 5x^2-17x=0 \\ \Leftrightarrow x(5x-17) = 0 \\ \Leftrightarrow x = 0 \vee 5x-17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{17}{5} \\ V = \Big\{ \frac{17}{5}; 0 \Big\} \\ -----------------\)
3. \(-2x^2-12x=5x^2+4x \\ \Leftrightarrow -7x^2-16x=0 \\ \Leftrightarrow x(-7x-16) = 0 \\ \Leftrightarrow x = 0 \vee -7x-16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{16}{-7} = \frac{-16}{7} \\ V = \Big\{ 0 ; \frac{-16}{7} \Big\} \\ -----------------\)
4. \(4x^2+17x=0 \\ \Leftrightarrow x(4x+17) = 0 \\ \Leftrightarrow x = 0 \vee 4x+17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-17}{4} \\ V = \Big\{ 0 ; \frac{-17}{4} \Big\} \\ -----------------\)
5. \(3(9x^2-7x)=-(-33x^2+2x) \\ \Leftrightarrow 27x^2-21x=33x^2-2x \\ \Leftrightarrow 27x^2-21x-33x^2+2x= 0 \\ \Leftrightarrow -6x^2+19x=0 \\ \Leftrightarrow x(-6x+19) = 0 \\ \Leftrightarrow x = 0 \vee -6x+19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-19}{-6} = \frac{19}{6} \\ V = \Big\{ \frac{19}{6}; 0 \Big\} \\ -----------------\)
6. \(5(9x^2-4x)=-(-44x^2+28x) \\ \Leftrightarrow 45x^2-20x=44x^2-28x \\ \Leftrightarrow 45x^2-20x-44x^2+28x= 0 \\ \Leftrightarrow x^2-8x=0 \\ \Leftrightarrow x(x-8) = 0 \\ \Leftrightarrow x = 0 \vee x-8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{8}{1} = 8 \\ V = \Big\{ 8; 0 \Big\} \\ -----------------\)
7. \(-3(-10x^2-9x)=-(-35x^2-50x) \\ \Leftrightarrow 30x^2+27x=35x^2+50x \\ \Leftrightarrow 30x^2+27x-35x^2-50x= 0 \\ \Leftrightarrow -5x^2+23x=0 \\ \Leftrightarrow x(-5x+23) = 0 \\ \Leftrightarrow x = 0 \vee -5x+23=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-23}{-5} = \frac{23}{5} \\ V = \Big\{ \frac{23}{5}; 0 \Big\} \\ -----------------\)
8. \(-x^2-33x=-8x^2-9x \\ \Leftrightarrow 7x^2-24x=0 \\ \Leftrightarrow x(7x-24) = 0 \\ \Leftrightarrow x = 0 \vee 7x-24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{24}{7} \\ V = \Big\{ \frac{24}{7}; 0 \Big\} \\ -----------------\)
9. \(-15x^2+31x=-9x^2+10x \\ \Leftrightarrow -6x^2+21x=0 \\ \Leftrightarrow x(-6x+21) = 0 \\ \Leftrightarrow x = 0 \vee -6x+21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-21}{-6} = \frac{7}{2} \\ V = \Big\{ \frac{7}{2}; 0 \Big\} \\ -----------------\)
10. \(3x^2-6x=0 \\ \Leftrightarrow x(3x-6) = 0 \\ \Leftrightarrow x = 0 \vee 3x-6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{6}{3} = 2 \\ V = \Big\{ 2; 0 \Big\} \\ -----------------\)
11. \(4(-4x^2-2x)=-(11x^2+5x) \\ \Leftrightarrow -16x^2-8x=-11x^2-5x \\ \Leftrightarrow -16x^2-8x+11x^2+5x= 0 \\ \Leftrightarrow -5x^2+3x=0 \\ \Leftrightarrow x(-5x+3) = 0 \\ \Leftrightarrow x = 0 \vee -5x+3=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-3}{-5} = \frac{3}{5} \\ V = \Big\{ \frac{3}{5}; 0 \Big\} \\ -----------------\)
12. \(-x^2-10x=0 \\ \Leftrightarrow x(-x-10) = 0 \\ \Leftrightarrow x = 0 \vee -x-10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{10}{-1} = -10 \\ V = \Big\{ 0 ; -10 \Big\} \\ -----------------\)