Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(5(7x^2+6x)=-(-37x^2-9x)\)
2. \(4x^2+7x=0\)
3. \(-3(7x^2-10x)=-(19x^2-27x)\)
4. \(2(8x^2+5x)=-(-11x^2+11x)\)
5. \(-2(-8x^2+3x)=-(-22x^2+31x)\)
6. \(-4(3x^2-3x)=-(18x^2+8x)\)
7. \(4(2x^2+5x)=-(-2x^2-22x)\)
8. \(-x^2-23x=0\)
9. \(3(-8x^2-2x)=-(28x^2+7x)\)
10. \(2(-7x^2+6x)=-(11x^2+10x)\)
11. \(-6x^2-24x=0\)
12. \(4(7x^2+9x)=-(-26x^2-44x)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(5(7x^2+6x)=-(-37x^2-9x) \\ \Leftrightarrow 35x^2+30x=37x^2+9x \\ \Leftrightarrow 35x^2+30x-37x^2-9x= 0 \\ \Leftrightarrow -2x^2-21x=0 \\ \Leftrightarrow x(-2x-21) = 0 \\ \Leftrightarrow x = 0 \vee -2x-21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{21}{-2} = \frac{-21}{2} \\ V = \Big\{ 0 ; \frac{-21}{2} \Big\} \\ -----------------\)
2. \(4x^2+7x=0 \\ \Leftrightarrow x(4x+7) = 0 \\ \Leftrightarrow x = 0 \vee 4x+7=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-7}{4} \\ V = \Big\{ 0 ; \frac{-7}{4} \Big\} \\ -----------------\)
3. \(-3(7x^2-10x)=-(19x^2-27x) \\ \Leftrightarrow -21x^2+30x=-19x^2+27x \\ \Leftrightarrow -21x^2+30x+19x^2-27x= 0 \\ \Leftrightarrow -2x^2-3x=0 \\ \Leftrightarrow x(-2x-3) = 0 \\ \Leftrightarrow x = 0 \vee -2x-3=0 \\ \Leftrightarrow x = 0 \vee x = \frac{3}{-2} = \frac{-3}{2} \\ V = \Big\{ 0 ; \frac{-3}{2} \Big\} \\ -----------------\)
4. \(2(8x^2+5x)=-(-11x^2+11x) \\ \Leftrightarrow 16x^2+10x=11x^2-11x \\ \Leftrightarrow 16x^2+10x-11x^2+11x= 0 \\ \Leftrightarrow 5x^2-21x=0 \\ \Leftrightarrow x(5x-21) = 0 \\ \Leftrightarrow x = 0 \vee 5x-21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{21}{5} \\ V = \Big\{ \frac{21}{5}; 0 \Big\} \\ -----------------\)
5. \(-2(-8x^2+3x)=-(-22x^2+31x) \\ \Leftrightarrow 16x^2-6x=22x^2-31x \\ \Leftrightarrow 16x^2-6x-22x^2+31x= 0 \\ \Leftrightarrow -6x^2-25x=0 \\ \Leftrightarrow x(-6x-25) = 0 \\ \Leftrightarrow x = 0 \vee -6x-25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{25}{-6} = \frac{-25}{6} \\ V = \Big\{ 0 ; \frac{-25}{6} \Big\} \\ -----------------\)
6. \(-4(3x^2-3x)=-(18x^2+8x) \\ \Leftrightarrow -12x^2+12x=-18x^2-8x \\ \Leftrightarrow -12x^2+12x+18x^2+8x= 0 \\ \Leftrightarrow 6x^2-20x=0 \\ \Leftrightarrow x(6x-20) = 0 \\ \Leftrightarrow x = 0 \vee 6x-20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{20}{6} = \frac{10}{3} \\ V = \Big\{ \frac{10}{3}; 0 \Big\} \\ -----------------\)
7. \(4(2x^2+5x)=-(-2x^2-22x) \\ \Leftrightarrow 8x^2+20x=2x^2+22x \\ \Leftrightarrow 8x^2+20x-2x^2-22x= 0 \\ \Leftrightarrow 6x^2+2x=0 \\ \Leftrightarrow x(6x+2) = 0 \\ \Leftrightarrow x = 0 \vee 6x+2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-2}{6} = \frac{-1}{3} \\ V = \Big\{ 0 ; \frac{-1}{3} \Big\} \\ -----------------\)
8. \(-x^2-23x=0 \\ \Leftrightarrow x(-x-23) = 0 \\ \Leftrightarrow x = 0 \vee -x-23=0 \\ \Leftrightarrow x = 0 \vee x = \frac{23}{-1} = -23 \\ V = \Big\{ 0 ; -23 \Big\} \\ -----------------\)
9. \(3(-8x^2-2x)=-(28x^2+7x) \\ \Leftrightarrow -24x^2-6x=-28x^2-7x \\ \Leftrightarrow -24x^2-6x+28x^2+7x= 0 \\ \Leftrightarrow 4x^2-1x=0 \\ \Leftrightarrow x(4x-1) = 0 \\ \Leftrightarrow x = 0 \vee 4x-1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{1}{4} \\ V = \Big\{ \frac{1}{4}; 0 \Big\} \\ -----------------\)
10. \(2(-7x^2+6x)=-(11x^2+10x) \\ \Leftrightarrow -14x^2+12x=-11x^2-10x \\ \Leftrightarrow -14x^2+12x+11x^2+10x= 0 \\ \Leftrightarrow -3x^2-22x=0 \\ \Leftrightarrow x(-3x-22) = 0 \\ \Leftrightarrow x = 0 \vee -3x-22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{22}{-3} = \frac{-22}{3} \\ V = \Big\{ 0 ; \frac{-22}{3} \Big\} \\ -----------------\)
11. \(-6x^2-24x=0 \\ \Leftrightarrow x(-6x-24) = 0 \\ \Leftrightarrow x = 0 \vee -6x-24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{24}{-6} = -4 \\ V = \Big\{ 0 ; -4 \Big\} \\ -----------------\)
12. \(4(7x^2+9x)=-(-26x^2-44x) \\ \Leftrightarrow 28x^2+36x=26x^2+44x \\ \Leftrightarrow 28x^2+36x-26x^2-44x= 0 \\ \Leftrightarrow 2x^2+8x=0 \\ \Leftrightarrow x(2x+8) = 0 \\ \Leftrightarrow x = 0 \vee 2x+8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-8}{2} = -4 \\ V = \Big\{ 0 ; -4 \Big\} \\ -----------------\)