Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-13x^2+22x=-6x^2+5x\)
2. \(-x^2-3x=-8x^2+5x\)
3. \(5(-6x^2-2x)=-(27x^2-8x)\)
4. \(3x^2-9x=5x^2+9x\)
5. \(-2(-3x^2-4x)=-(-11x^2+12x)\)
6. \(5(9x^2-9x)=-(-44x^2+39x)\)
7. \(-x^2+5x=0\)
8. \(-2(-5x^2-6x)=-(-6x^2+x)\)
9. \(14x^2-9x=9x^2-8x\)
10. \(-x^2+22x=0\)
11. \(3x^2+5x=-3x^2+7x\)
12. \(-13x^2+14x=-5x^2-4x\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-13x^2+22x=-6x^2+5x \\ \Leftrightarrow -7x^2+17x=0 \\ \Leftrightarrow x(-7x+17) = 0 \\ \Leftrightarrow x = 0 \vee -7x+17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-17}{-7} = \frac{17}{7} \\ V = \Big\{ \frac{17}{7}; 0 \Big\} \\ -----------------\)
2. \(-x^2-3x=-8x^2+5x \\ \Leftrightarrow 7x^2-8x=0 \\ \Leftrightarrow x(7x-8) = 0 \\ \Leftrightarrow x = 0 \vee 7x-8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{8}{7} \\ V = \Big\{ \frac{8}{7}; 0 \Big\} \\ -----------------\)
3. \(5(-6x^2-2x)=-(27x^2-8x) \\ \Leftrightarrow -30x^2-10x=-27x^2+8x \\ \Leftrightarrow -30x^2-10x+27x^2-8x= 0 \\ \Leftrightarrow -3x^2+18x=0 \\ \Leftrightarrow x(-3x+18) = 0 \\ \Leftrightarrow x = 0 \vee -3x+18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-18}{-3} = 6 \\ V = \Big\{ 6; 0 \Big\} \\ -----------------\)
4. \(3x^2-9x=5x^2+9x \\ \Leftrightarrow -2x^2-18x=0 \\ \Leftrightarrow x(-2x-18) = 0 \\ \Leftrightarrow x = 0 \vee -2x-18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{18}{-2} = -9 \\ V = \Big\{ 0 ; -9 \Big\} \\ -----------------\)
5. \(-2(-3x^2-4x)=-(-11x^2+12x) \\ \Leftrightarrow 6x^2+8x=11x^2-12x \\ \Leftrightarrow 6x^2+8x-11x^2+12x= 0 \\ \Leftrightarrow -5x^2-20x=0 \\ \Leftrightarrow x(-5x-20) = 0 \\ \Leftrightarrow x = 0 \vee -5x-20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{20}{-5} = -4 \\ V = \Big\{ 0 ; -4 \Big\} \\ -----------------\)
6. \(5(9x^2-9x)=-(-44x^2+39x) \\ \Leftrightarrow 45x^2-45x=44x^2-39x \\ \Leftrightarrow 45x^2-45x-44x^2+39x= 0 \\ \Leftrightarrow x^2+6x=0 \\ \Leftrightarrow x(x+6) = 0 \\ \Leftrightarrow x = 0 \vee x+6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-6}{1} = -6 \\ V = \Big\{ 0 ; -6 \Big\} \\ -----------------\)
7. \(-x^2+5x=0 \\ \Leftrightarrow x(-x+5) = 0 \\ \Leftrightarrow x = 0 \vee -x+5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-5}{-1} = 5 \\ V = \Big\{ 5; 0 \Big\} \\ -----------------\)
8. \(-2(-5x^2-6x)=-(-6x^2+x) \\ \Leftrightarrow 10x^2+12x=6x^2-x \\ \Leftrightarrow 10x^2+12x-6x^2+x= 0 \\ \Leftrightarrow 4x^2-13x=0 \\ \Leftrightarrow x(4x-13) = 0 \\ \Leftrightarrow x = 0 \vee 4x-13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{13}{4} \\ V = \Big\{ \frac{13}{4}; 0 \Big\} \\ -----------------\)
9. \(14x^2-9x=9x^2-8x \\ \Leftrightarrow 5x^2-1x=0 \\ \Leftrightarrow x(5x-1) = 0 \\ \Leftrightarrow x = 0 \vee 5x-1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{1}{5} \\ V = \Big\{ \frac{1}{5}; 0 \Big\} \\ -----------------\)
10. \(-x^2+22x=0 \\ \Leftrightarrow x(-x+22) = 0 \\ \Leftrightarrow x = 0 \vee -x+22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-22}{-1} = 22 \\ V = \Big\{ 22; 0 \Big\} \\ -----------------\)
11. \(3x^2+5x=-3x^2+7x \\ \Leftrightarrow 6x^2-2x=0 \\ \Leftrightarrow x(6x-2) = 0 \\ \Leftrightarrow x = 0 \vee 6x-2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{2}{6} = \frac{1}{3} \\ V = \Big\{ \frac{1}{3}; 0 \Big\} \\ -----------------\)
12. \(-13x^2+14x=-5x^2-4x \\ \Leftrightarrow -8x^2+18x=0 \\ \Leftrightarrow x(-8x+18) = 0 \\ \Leftrightarrow x = 0 \vee -8x+18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-18}{-8} = \frac{9}{4} \\ V = \Big\{ \frac{9}{4}; 0 \Big\} \\ -----------------\)