Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(x^2+3x=7x^2-3x\)
2. \(4x^2+1x=0\)
3. \(7x^2+6x=2x^2+5x\)
4. \(-7x^2+12x=0\)
5. \(3(-10x^2-2x)=-(29x^2+26x)\)
6. \(-2(-6x^2+2x)=-(-16x^2-20x)\)
7. \(-5(9x^2-5x)=-(41x^2-39x)\)
8. \(x^2-6x=8x^2+5x\)
9. \(-5x^2+19x=0\)
10. \(10x^2+14x=2x^2+4x\)
11. \(5(4x^2-4x)=-(-14x^2+21x)\)
12. \(3(4x^2+10x)=-(-19x^2-38x)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(x^2+3x=7x^2-3x \\ \Leftrightarrow -6x^2+6x=0 \\ \Leftrightarrow x(-6x+6) = 0 \\ \Leftrightarrow x = 0 \vee -6x+6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-6}{-6} = 1 \\ V = \Big\{ 1; 0 \Big\} \\ -----------------\)
2. \(4x^2+1x=0 \\ \Leftrightarrow x(4x+1) = 0 \\ \Leftrightarrow x = 0 \vee 4x+1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-1}{4} \\ V = \Big\{ 0 ; \frac{-1}{4} \Big\} \\ -----------------\)
3. \(7x^2+6x=2x^2+5x \\ \Leftrightarrow 5x^2+1x=0 \\ \Leftrightarrow x(5x+1) = 0 \\ \Leftrightarrow x = 0 \vee 5x+1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-1}{5} \\ V = \Big\{ 0 ; \frac{-1}{5} \Big\} \\ -----------------\)
4. \(-7x^2+12x=0 \\ \Leftrightarrow x(-7x+12) = 0 \\ \Leftrightarrow x = 0 \vee -7x+12=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-12}{-7} = \frac{12}{7} \\ V = \Big\{ \frac{12}{7}; 0 \Big\} \\ -----------------\)
5. \(3(-10x^2-2x)=-(29x^2+26x) \\ \Leftrightarrow -30x^2-6x=-29x^2-26x \\ \Leftrightarrow -30x^2-6x+29x^2+26x= 0 \\ \Leftrightarrow -x^2-20x=0 \\ \Leftrightarrow x(-x-20) = 0 \\ \Leftrightarrow x = 0 \vee -x-20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{20}{-1} = -20 \\ V = \Big\{ 0 ; -20 \Big\} \\ -----------------\)
6. \(-2(-6x^2+2x)=-(-16x^2-20x) \\ \Leftrightarrow 12x^2-4x=16x^2+20x \\ \Leftrightarrow 12x^2-4x-16x^2-20x= 0 \\ \Leftrightarrow -4x^2+24x=0 \\ \Leftrightarrow x(-4x+24) = 0 \\ \Leftrightarrow x = 0 \vee -4x+24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-24}{-4} = 6 \\ V = \Big\{ 6; 0 \Big\} \\ -----------------\)
7. \(-5(9x^2-5x)=-(41x^2-39x) \\ \Leftrightarrow -45x^2+25x=-41x^2+39x \\ \Leftrightarrow -45x^2+25x+41x^2-39x= 0 \\ \Leftrightarrow -4x^2+14x=0 \\ \Leftrightarrow x(-4x+14) = 0 \\ \Leftrightarrow x = 0 \vee -4x+14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-14}{-4} = \frac{7}{2} \\ V = \Big\{ \frac{7}{2}; 0 \Big\} \\ -----------------\)
8. \(x^2-6x=8x^2+5x \\ \Leftrightarrow -7x^2-11x=0 \\ \Leftrightarrow x(-7x-11) = 0 \\ \Leftrightarrow x = 0 \vee -7x-11=0 \\ \Leftrightarrow x = 0 \vee x = \frac{11}{-7} = \frac{-11}{7} \\ V = \Big\{ 0 ; \frac{-11}{7} \Big\} \\ -----------------\)
9. \(-5x^2+19x=0 \\ \Leftrightarrow x(-5x+19) = 0 \\ \Leftrightarrow x = 0 \vee -5x+19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-19}{-5} = \frac{19}{5} \\ V = \Big\{ \frac{19}{5}; 0 \Big\} \\ -----------------\)
10. \(10x^2+14x=2x^2+4x \\ \Leftrightarrow 8x^2+10x=0 \\ \Leftrightarrow x(8x+10) = 0 \\ \Leftrightarrow x = 0 \vee 8x+10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-10}{8} = \frac{-5}{4} \\ V = \Big\{ 0 ; \frac{-5}{4} \Big\} \\ -----------------\)
11. \(5(4x^2-4x)=-(-14x^2+21x) \\ \Leftrightarrow 20x^2-20x=14x^2-21x \\ \Leftrightarrow 20x^2-20x-14x^2+21x= 0 \\ \Leftrightarrow 6x^2-1x=0 \\ \Leftrightarrow x(6x-1) = 0 \\ \Leftrightarrow x = 0 \vee 6x-1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{1}{6} \\ V = \Big\{ \frac{1}{6}; 0 \Big\} \\ -----------------\)
12. \(3(4x^2+10x)=-(-19x^2-38x) \\ \Leftrightarrow 12x^2+30x=19x^2+38x \\ \Leftrightarrow 12x^2+30x-19x^2-38x= 0 \\ \Leftrightarrow -7x^2+8x=0 \\ \Leftrightarrow x(-7x+8) = 0 \\ \Leftrightarrow x = 0 \vee -7x+8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-8}{-7} = \frac{8}{7} \\ V = \Big\{ \frac{8}{7}; 0 \Big\} \\ -----------------\)