Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-5(10x^2-8x)=-(53x^2-20x)\)
2. \(14x^2+5x=10x^2+8x\)
3. \(-2x^2-19x=0\)
4. \(-3(8x^2+5x)=-(31x^2+13x)\)
5. \(-2(10x^2+4x)=-(22x^2+31x)\)
6. \(-8x^2-5x=0\)
7. \(18x^2+2x=10x^2-8x\)
8. \(-2(8x^2+5x)=-(20x^2-2x)\)
9. \(5(-5x^2-6x)=-(28x^2+21x)\)
10. \(14x^2-6x=6x^2+4x\)
11. \(-4x^2+14x=0\)
12. \(3x^2+x=-4x^2+3x\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-5(10x^2-8x)=-(53x^2-20x) \\ \Leftrightarrow -50x^2+40x=-53x^2+20x \\ \Leftrightarrow -50x^2+40x+53x^2-20x= 0 \\ \Leftrightarrow 3x^2-20x=0 \\ \Leftrightarrow x(3x-20) = 0 \\ \Leftrightarrow x = 0 \vee 3x-20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{20}{3} \\ V = \Big\{ \frac{20}{3}; 0 \Big\} \\ -----------------\)
2. \(14x^2+5x=10x^2+8x \\ \Leftrightarrow 4x^2-3x=0 \\ \Leftrightarrow x(4x-3) = 0 \\ \Leftrightarrow x = 0 \vee 4x-3=0 \\ \Leftrightarrow x = 0 \vee x = \frac{3}{4} \\ V = \Big\{ \frac{3}{4}; 0 \Big\} \\ -----------------\)
3. \(-2x^2-19x=0 \\ \Leftrightarrow x(-2x-19) = 0 \\ \Leftrightarrow x = 0 \vee -2x-19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{19}{-2} = \frac{-19}{2} \\ V = \Big\{ 0 ; \frac{-19}{2} \Big\} \\ -----------------\)
4. \(-3(8x^2+5x)=-(31x^2+13x) \\ \Leftrightarrow -24x^2-15x=-31x^2-13x \\ \Leftrightarrow -24x^2-15x+31x^2+13x= 0 \\ \Leftrightarrow 7x^2+2x=0 \\ \Leftrightarrow x(7x+2) = 0 \\ \Leftrightarrow x = 0 \vee 7x+2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-2}{7} \\ V = \Big\{ 0 ; \frac{-2}{7} \Big\} \\ -----------------\)
5. \(-2(10x^2+4x)=-(22x^2+31x) \\ \Leftrightarrow -20x^2-8x=-22x^2-31x \\ \Leftrightarrow -20x^2-8x+22x^2+31x= 0 \\ \Leftrightarrow 2x^2-23x=0 \\ \Leftrightarrow x(2x-23) = 0 \\ \Leftrightarrow x = 0 \vee 2x-23=0 \\ \Leftrightarrow x = 0 \vee x = \frac{23}{2} \\ V = \Big\{ \frac{23}{2}; 0 \Big\} \\ -----------------\)
6. \(-8x^2-5x=0 \\ \Leftrightarrow x(-8x-5) = 0 \\ \Leftrightarrow x = 0 \vee -8x-5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{5}{-8} = \frac{-5}{8} \\ V = \Big\{ 0 ; \frac{-5}{8} \Big\} \\ -----------------\)
7. \(18x^2+2x=10x^2-8x \\ \Leftrightarrow 8x^2+10x=0 \\ \Leftrightarrow x(8x+10) = 0 \\ \Leftrightarrow x = 0 \vee 8x+10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-10}{8} = \frac{-5}{4} \\ V = \Big\{ 0 ; \frac{-5}{4} \Big\} \\ -----------------\)
8. \(-2(8x^2+5x)=-(20x^2-2x) \\ \Leftrightarrow -16x^2-10x=-20x^2+2x \\ \Leftrightarrow -16x^2-10x+20x^2-2x= 0 \\ \Leftrightarrow 4x^2+12x=0 \\ \Leftrightarrow x(4x+12) = 0 \\ \Leftrightarrow x = 0 \vee 4x+12=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-12}{4} = -3 \\ V = \Big\{ 0 ; -3 \Big\} \\ -----------------\)
9. \(5(-5x^2-6x)=-(28x^2+21x) \\ \Leftrightarrow -25x^2-30x=-28x^2-21x \\ \Leftrightarrow -25x^2-30x+28x^2+21x= 0 \\ \Leftrightarrow 3x^2+9x=0 \\ \Leftrightarrow x(3x+9) = 0 \\ \Leftrightarrow x = 0 \vee 3x+9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-9}{3} = -3 \\ V = \Big\{ 0 ; -3 \Big\} \\ -----------------\)
10. \(14x^2-6x=6x^2+4x \\ \Leftrightarrow 8x^2-10x=0 \\ \Leftrightarrow x(8x-10) = 0 \\ \Leftrightarrow x = 0 \vee 8x-10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{10}{8} = \frac{5}{4} \\ V = \Big\{ \frac{5}{4}; 0 \Big\} \\ -----------------\)
11. \(-4x^2+14x=0 \\ \Leftrightarrow x(-4x+14) = 0 \\ \Leftrightarrow x = 0 \vee -4x+14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-14}{-4} = \frac{7}{2} \\ V = \Big\{ \frac{7}{2}; 0 \Big\} \\ -----------------\)
12. \(3x^2+x=-4x^2+3x \\ \Leftrightarrow 7x^2-2x=0 \\ \Leftrightarrow x(7x-2) = 0 \\ \Leftrightarrow x = 0 \vee 7x-2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{2}{7} \\ V = \Big\{ \frac{2}{7}; 0 \Big\} \\ -----------------\)