Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-6x^2-28x=-8x^2-6x\)
2. \(17x^2+13x=9x^2-4x\)
3. \(x^2+13x=-7x^2-10x\)
4. \(4(-9x^2+8x)=-(37x^2-55x)\)
5. \(2x^2+10x=0\)
6. \(5(-9x^2+8x)=-(41x^2-50x)\)
7. \(-2x^2+10x=0\)
8. \(-5x^2-19x=-3x^2+2x\)
9. \(-6x^2-3x=0\)
10. \(3(-4x^2-5x)=-(4x^2-10x)\)
11. \(-3(5x^2+3x)=-(12x^2+33x)\)
12. \(7x^2-21x=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-6x^2-28x=-8x^2-6x \\ \Leftrightarrow 2x^2-22x=0 \\ \Leftrightarrow x(2x-22) = 0 \\ \Leftrightarrow x = 0 \vee 2x-22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{22}{2} = 11 \\ V = \Big\{ 11; 0 \Big\} \\ -----------------\)
2. \(17x^2+13x=9x^2-4x \\ \Leftrightarrow 8x^2+17x=0 \\ \Leftrightarrow x(8x+17) = 0 \\ \Leftrightarrow x = 0 \vee 8x+17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-17}{8} \\ V = \Big\{ 0 ; \frac{-17}{8} \Big\} \\ -----------------\)
3. \(x^2+13x=-7x^2-10x \\ \Leftrightarrow 8x^2+23x=0 \\ \Leftrightarrow x(8x+23) = 0 \\ \Leftrightarrow x = 0 \vee 8x+23=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-23}{8} \\ V = \Big\{ 0 ; \frac{-23}{8} \Big\} \\ -----------------\)
4. \(4(-9x^2+8x)=-(37x^2-55x) \\ \Leftrightarrow -36x^2+32x=-37x^2+55x \\ \Leftrightarrow -36x^2+32x+37x^2-55x= 0 \\ \Leftrightarrow x^2+23x=0 \\ \Leftrightarrow x(x+23) = 0 \\ \Leftrightarrow x = 0 \vee x+23=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-23}{1} = -23 \\ V = \Big\{ 0 ; -23 \Big\} \\ -----------------\)
5. \(2x^2+10x=0 \\ \Leftrightarrow x(2x+10) = 0 \\ \Leftrightarrow x = 0 \vee 2x+10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-10}{2} = -5 \\ V = \Big\{ 0 ; -5 \Big\} \\ -----------------\)
6. \(5(-9x^2+8x)=-(41x^2-50x) \\ \Leftrightarrow -45x^2+40x=-41x^2+50x \\ \Leftrightarrow -45x^2+40x+41x^2-50x= 0 \\ \Leftrightarrow -4x^2+10x=0 \\ \Leftrightarrow x(-4x+10) = 0 \\ \Leftrightarrow x = 0 \vee -4x+10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-10}{-4} = \frac{5}{2} \\ V = \Big\{ \frac{5}{2}; 0 \Big\} \\ -----------------\)
7. \(-2x^2+10x=0 \\ \Leftrightarrow x(-2x+10) = 0 \\ \Leftrightarrow x = 0 \vee -2x+10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-10}{-2} = 5 \\ V = \Big\{ 5; 0 \Big\} \\ -----------------\)
8. \(-5x^2-19x=-3x^2+2x \\ \Leftrightarrow -2x^2-21x=0 \\ \Leftrightarrow x(-2x-21) = 0 \\ \Leftrightarrow x = 0 \vee -2x-21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{21}{-2} = \frac{-21}{2} \\ V = \Big\{ 0 ; \frac{-21}{2} \Big\} \\ -----------------\)
9. \(-6x^2-3x=0 \\ \Leftrightarrow x(-6x-3) = 0 \\ \Leftrightarrow x = 0 \vee -6x-3=0 \\ \Leftrightarrow x = 0 \vee x = \frac{3}{-6} = \frac{-1}{2} \\ V = \Big\{ 0 ; \frac{-1}{2} \Big\} \\ -----------------\)
10. \(3(-4x^2-5x)=-(4x^2-10x) \\ \Leftrightarrow -12x^2-15x=-4x^2+10x \\ \Leftrightarrow -12x^2-15x+4x^2-10x= 0 \\ \Leftrightarrow -8x^2+25x=0 \\ \Leftrightarrow x(-8x+25) = 0 \\ \Leftrightarrow x = 0 \vee -8x+25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-25}{-8} = \frac{25}{8} \\ V = \Big\{ \frac{25}{8}; 0 \Big\} \\ -----------------\)
11. \(-3(5x^2+3x)=-(12x^2+33x) \\ \Leftrightarrow -15x^2-9x=-12x^2-33x \\ \Leftrightarrow -15x^2-9x+12x^2+33x= 0 \\ \Leftrightarrow -3x^2-24x=0 \\ \Leftrightarrow x(-3x-24) = 0 \\ \Leftrightarrow x = 0 \vee -3x-24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{24}{-3} = -8 \\ V = \Big\{ 0 ; -8 \Big\} \\ -----------------\)
12. \(7x^2-21x=0 \\ \Leftrightarrow x(7x-21) = 0 \\ \Leftrightarrow x = 0 \vee 7x-21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{21}{7} = 3 \\ V = \Big\{ 3; 0 \Big\} \\ -----------------\)