Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-4x^2-19x=0\)
2. \(-x^2-18x=2x^2+6x\)
3. \(-5(8x^2-7x)=-(37x^2-49x)\)
4. \(-4(-3x^2-6x)=-(-16x^2-33x)\)
5. \(-x^2-12x=-7x^2-3x\)
6. \(-5(5x^2+3x)=-(19x^2+21x)\)
7. \(x^2-5x=-2x^2+4x\)
8. \(-12x^2+12x=-5x^2+10x\)
9. \(-6x^2+17x=-7x^2-7x\)
10. \(x^2-16x=4x^2-4x\)
11. \(3x^2-24x=-4x^2-8x\)
12. \(5(-6x^2+2x)=-(23x^2-25x)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-4x^2-19x=0 \\ \Leftrightarrow x(-4x-19) = 0 \\ \Leftrightarrow x = 0 \vee -4x-19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{19}{-4} = \frac{-19}{4} \\ V = \Big\{ 0 ; \frac{-19}{4} \Big\} \\ -----------------\)
2. \(-x^2-18x=2x^2+6x \\ \Leftrightarrow -3x^2-24x=0 \\ \Leftrightarrow x(-3x-24) = 0 \\ \Leftrightarrow x = 0 \vee -3x-24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{24}{-3} = -8 \\ V = \Big\{ 0 ; -8 \Big\} \\ -----------------\)
3. \(-5(8x^2-7x)=-(37x^2-49x) \\ \Leftrightarrow -40x^2+35x=-37x^2+49x \\ \Leftrightarrow -40x^2+35x+37x^2-49x= 0 \\ \Leftrightarrow -3x^2+14x=0 \\ \Leftrightarrow x(-3x+14) = 0 \\ \Leftrightarrow x = 0 \vee -3x+14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-14}{-3} = \frac{14}{3} \\ V = \Big\{ \frac{14}{3}; 0 \Big\} \\ -----------------\)
4. \(-4(-3x^2-6x)=-(-16x^2-33x) \\ \Leftrightarrow 12x^2+24x=16x^2+33x \\ \Leftrightarrow 12x^2+24x-16x^2-33x= 0 \\ \Leftrightarrow -4x^2+9x=0 \\ \Leftrightarrow x(-4x+9) = 0 \\ \Leftrightarrow x = 0 \vee -4x+9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-9}{-4} = \frac{9}{4} \\ V = \Big\{ \frac{9}{4}; 0 \Big\} \\ -----------------\)
5. \(-x^2-12x=-7x^2-3x \\ \Leftrightarrow 6x^2-9x=0 \\ \Leftrightarrow x(6x-9) = 0 \\ \Leftrightarrow x = 0 \vee 6x-9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{9}{6} = \frac{3}{2} \\ V = \Big\{ \frac{3}{2}; 0 \Big\} \\ -----------------\)
6. \(-5(5x^2+3x)=-(19x^2+21x) \\ \Leftrightarrow -25x^2-15x=-19x^2-21x \\ \Leftrightarrow -25x^2-15x+19x^2+21x= 0 \\ \Leftrightarrow -6x^2-6x=0 \\ \Leftrightarrow x(-6x-6) = 0 \\ \Leftrightarrow x = 0 \vee -6x-6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{6}{-6} = -1 \\ V = \Big\{ 0 ; -1 \Big\} \\ -----------------\)
7. \(x^2-5x=-2x^2+4x \\ \Leftrightarrow 3x^2-9x=0 \\ \Leftrightarrow x(3x-9) = 0 \\ \Leftrightarrow x = 0 \vee 3x-9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{9}{3} = 3 \\ V = \Big\{ 3; 0 \Big\} \\ -----------------\)
8. \(-12x^2+12x=-5x^2+10x \\ \Leftrightarrow -7x^2+2x=0 \\ \Leftrightarrow x(-7x+2) = 0 \\ \Leftrightarrow x = 0 \vee -7x+2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-2}{-7} = \frac{2}{7} \\ V = \Big\{ \frac{2}{7}; 0 \Big\} \\ -----------------\)
9. \(-6x^2+17x=-7x^2-7x \\ \Leftrightarrow x^2+24x=0 \\ \Leftrightarrow x(x+24) = 0 \\ \Leftrightarrow x = 0 \vee x+24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-24}{1} = -24 \\ V = \Big\{ 0 ; -24 \Big\} \\ -----------------\)
10. \(x^2-16x=4x^2-4x \\ \Leftrightarrow -3x^2-12x=0 \\ \Leftrightarrow x(-3x-12) = 0 \\ \Leftrightarrow x = 0 \vee -3x-12=0 \\ \Leftrightarrow x = 0 \vee x = \frac{12}{-3} = -4 \\ V = \Big\{ 0 ; -4 \Big\} \\ -----------------\)
11. \(3x^2-24x=-4x^2-8x \\ \Leftrightarrow 7x^2-16x=0 \\ \Leftrightarrow x(7x-16) = 0 \\ \Leftrightarrow x = 0 \vee 7x-16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{16}{7} \\ V = \Big\{ \frac{16}{7}; 0 \Big\} \\ -----------------\)
12. \(5(-6x^2+2x)=-(23x^2-25x) \\ \Leftrightarrow -30x^2+10x=-23x^2+25x \\ \Leftrightarrow -30x^2+10x+23x^2-25x= 0 \\ \Leftrightarrow -7x^2+15x=0 \\ \Leftrightarrow x(-7x+15) = 0 \\ \Leftrightarrow x = 0 \vee -7x+15=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-15}{-7} = \frac{15}{7} \\ V = \Big\{ \frac{15}{7}; 0 \Big\} \\ -----------------\)