Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-7x^2+8x=0\)
2. \(15x^2-16x=7x^2-5x\)
3. \(3(-4x^2-8x)=-(5x^2+0x)\)
4. \(-3(-4x^2+4x)=-(-15x^2+14x)\)
5. \(3x^2-12x=-2x^2+7x\)
6. \(-x^2-21x=-4x^2+2x\)
7. \(-7x^2+10x=0\)
8. \(-4x^2+15x=2x^2+10x\)
9. \(-3(5x^2+9x)=-(18x^2+29x)\)
10. \(3(-7x^2-2x)=-(24x^2-7x)\)
11. \(-2x^2-17x=-5x^2-5x\)
12. \(11x^2+25x=3x^2+10x\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-7x^2+8x=0 \\ \Leftrightarrow x(-7x+8) = 0 \\ \Leftrightarrow x = 0 \vee -7x+8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-8}{-7} = \frac{8}{7} \\ V = \Big\{ \frac{8}{7}; 0 \Big\} \\ -----------------\)
2. \(15x^2-16x=7x^2-5x \\ \Leftrightarrow 8x^2-11x=0 \\ \Leftrightarrow x(8x-11) = 0 \\ \Leftrightarrow x = 0 \vee 8x-11=0 \\ \Leftrightarrow x = 0 \vee x = \frac{11}{8} \\ V = \Big\{ \frac{11}{8}; 0 \Big\} \\ -----------------\)
3. \(3(-4x^2-8x)=-(5x^2+0x) \\ \Leftrightarrow -12x^2-24x=-5x^2+0x \\ \Leftrightarrow -12x^2-24x+5x^2+0x= 0 \\ \Leftrightarrow -7x^2+24x=0 \\ \Leftrightarrow x(-7x+24) = 0 \\ \Leftrightarrow x = 0 \vee -7x+24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-24}{-7} = \frac{24}{7} \\ V = \Big\{ \frac{24}{7}; 0 \Big\} \\ -----------------\)
4. \(-3(-4x^2+4x)=-(-15x^2+14x) \\ \Leftrightarrow 12x^2-12x=15x^2-14x \\ \Leftrightarrow 12x^2-12x-15x^2+14x= 0 \\ \Leftrightarrow -3x^2-2x=0 \\ \Leftrightarrow x(-3x-2) = 0 \\ \Leftrightarrow x = 0 \vee -3x-2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{2}{-3} = \frac{-2}{3} \\ V = \Big\{ 0 ; \frac{-2}{3} \Big\} \\ -----------------\)
5. \(3x^2-12x=-2x^2+7x \\ \Leftrightarrow 5x^2-19x=0 \\ \Leftrightarrow x(5x-19) = 0 \\ \Leftrightarrow x = 0 \vee 5x-19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{19}{5} \\ V = \Big\{ \frac{19}{5}; 0 \Big\} \\ -----------------\)
6. \(-x^2-21x=-4x^2+2x \\ \Leftrightarrow 3x^2-23x=0 \\ \Leftrightarrow x(3x-23) = 0 \\ \Leftrightarrow x = 0 \vee 3x-23=0 \\ \Leftrightarrow x = 0 \vee x = \frac{23}{3} \\ V = \Big\{ \frac{23}{3}; 0 \Big\} \\ -----------------\)
7. \(-7x^2+10x=0 \\ \Leftrightarrow x(-7x+10) = 0 \\ \Leftrightarrow x = 0 \vee -7x+10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-10}{-7} = \frac{10}{7} \\ V = \Big\{ \frac{10}{7}; 0 \Big\} \\ -----------------\)
8. \(-4x^2+15x=2x^2+10x \\ \Leftrightarrow -6x^2+5x=0 \\ \Leftrightarrow x(-6x+5) = 0 \\ \Leftrightarrow x = 0 \vee -6x+5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-5}{-6} = \frac{5}{6} \\ V = \Big\{ \frac{5}{6}; 0 \Big\} \\ -----------------\)
9. \(-3(5x^2+9x)=-(18x^2+29x) \\ \Leftrightarrow -15x^2-27x=-18x^2-29x \\ \Leftrightarrow -15x^2-27x+18x^2+29x= 0 \\ \Leftrightarrow 3x^2-2x=0 \\ \Leftrightarrow x(3x-2) = 0 \\ \Leftrightarrow x = 0 \vee 3x-2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{2}{3} \\ V = \Big\{ \frac{2}{3}; 0 \Big\} \\ -----------------\)
10. \(3(-7x^2-2x)=-(24x^2-7x) \\ \Leftrightarrow -21x^2-6x=-24x^2+7x \\ \Leftrightarrow -21x^2-6x+24x^2-7x= 0 \\ \Leftrightarrow 3x^2+13x=0 \\ \Leftrightarrow x(3x+13) = 0 \\ \Leftrightarrow x = 0 \vee 3x+13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-13}{3} \\ V = \Big\{ 0 ; \frac{-13}{3} \Big\} \\ -----------------\)
11. \(-2x^2-17x=-5x^2-5x \\ \Leftrightarrow 3x^2-12x=0 \\ \Leftrightarrow x(3x-12) = 0 \\ \Leftrightarrow x = 0 \vee 3x-12=0 \\ \Leftrightarrow x = 0 \vee x = \frac{12}{3} = 4 \\ V = \Big\{ 4; 0 \Big\} \\ -----------------\)
12. \(11x^2+25x=3x^2+10x \\ \Leftrightarrow 8x^2+15x=0 \\ \Leftrightarrow x(8x+15) = 0 \\ \Leftrightarrow x = 0 \vee 8x+15=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-15}{8} \\ V = \Big\{ 0 ; \frac{-15}{8} \Big\} \\ -----------------\)