Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-2(-10x^2+5x)=-(-28x^2+24x)\)
2. \(-6x^2+3x=0\)
3. \(3(-8x^2+4x)=-(31x^2-30x)\)
4. \(-2(-8x^2-9x)=-(-17x^2-7x)\)
5. \(-6x^2+0x=0\)
6. \(9x^2+5x=5x^2+6x\)
7. \(-2(7x^2+3x)=-(20x^2+8x)\)
8. \(4(-2x^2+6x)=-(15x^2-33x)\)
9. \(7x^2+8x=0\)
10. \(-4(-7x^2+9x)=-(-29x^2+30x)\)
11. \(2(5x^2+5x)=-(-3x^2-7x)\)
12. \(2x^2+6x=4x^2-7x\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-2(-10x^2+5x)=-(-28x^2+24x) \\ \Leftrightarrow 20x^2-10x=28x^2-24x \\ \Leftrightarrow 20x^2-10x-28x^2+24x= 0 \\ \Leftrightarrow -8x^2-14x=0 \\ \Leftrightarrow x(-8x-14) = 0 \\ \Leftrightarrow x = 0 \vee -8x-14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{14}{-8} = \frac{-7}{4} \\ V = \Big\{ 0 ; \frac{-7}{4} \Big\} \\ -----------------\)
2. \(-6x^2+3x=0 \\ \Leftrightarrow x(-6x+3) = 0 \\ \Leftrightarrow x = 0 \vee -6x+3=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-3}{-6} = \frac{1}{2} \\ V = \Big\{ \frac{1}{2}; 0 \Big\} \\ -----------------\)
3. \(3(-8x^2+4x)=-(31x^2-30x) \\ \Leftrightarrow -24x^2+12x=-31x^2+30x \\ \Leftrightarrow -24x^2+12x+31x^2-30x= 0 \\ \Leftrightarrow 7x^2+18x=0 \\ \Leftrightarrow x(7x+18) = 0 \\ \Leftrightarrow x = 0 \vee 7x+18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-18}{7} \\ V = \Big\{ 0 ; \frac{-18}{7} \Big\} \\ -----------------\)
4. \(-2(-8x^2-9x)=-(-17x^2-7x) \\ \Leftrightarrow 16x^2+18x=17x^2+7x \\ \Leftrightarrow 16x^2+18x-17x^2-7x= 0 \\ \Leftrightarrow -x^2-11x=0 \\ \Leftrightarrow x(-x-11) = 0 \\ \Leftrightarrow x = 0 \vee -x-11=0 \\ \Leftrightarrow x = 0 \vee x = \frac{11}{-1} = -11 \\ V = \Big\{ 0 ; -11 \Big\} \\ -----------------\)
5. \(-6x^2+0x=0 \\ \Leftrightarrow -6x^2=0 \\ \Leftrightarrow x^2 = \frac{0}{-6} \\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
6. \(9x^2+5x=5x^2+6x \\ \Leftrightarrow 4x^2-1x=0 \\ \Leftrightarrow x(4x-1) = 0 \\ \Leftrightarrow x = 0 \vee 4x-1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{1}{4} \\ V = \Big\{ \frac{1}{4}; 0 \Big\} \\ -----------------\)
7. \(-2(7x^2+3x)=-(20x^2+8x) \\ \Leftrightarrow -14x^2-6x=-20x^2-8x \\ \Leftrightarrow -14x^2-6x+20x^2+8x= 0 \\ \Leftrightarrow 6x^2-2x=0 \\ \Leftrightarrow x(6x-2) = 0 \\ \Leftrightarrow x = 0 \vee 6x-2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{2}{6} = \frac{1}{3} \\ V = \Big\{ \frac{1}{3}; 0 \Big\} \\ -----------------\)
8. \(4(-2x^2+6x)=-(15x^2-33x) \\ \Leftrightarrow -8x^2+24x=-15x^2+33x \\ \Leftrightarrow -8x^2+24x+15x^2-33x= 0 \\ \Leftrightarrow 7x^2+9x=0 \\ \Leftrightarrow x(7x+9) = 0 \\ \Leftrightarrow x = 0 \vee 7x+9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-9}{7} \\ V = \Big\{ 0 ; \frac{-9}{7} \Big\} \\ -----------------\)
9. \(7x^2+8x=0 \\ \Leftrightarrow x(7x+8) = 0 \\ \Leftrightarrow x = 0 \vee 7x+8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-8}{7} \\ V = \Big\{ 0 ; \frac{-8}{7} \Big\} \\ -----------------\)
10. \(-4(-7x^2+9x)=-(-29x^2+30x) \\ \Leftrightarrow 28x^2-36x=29x^2-30x \\ \Leftrightarrow 28x^2-36x-29x^2+30x= 0 \\ \Leftrightarrow -x^2+6x=0 \\ \Leftrightarrow x(-x+6) = 0 \\ \Leftrightarrow x = 0 \vee -x+6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-6}{-1} = 6 \\ V = \Big\{ 6; 0 \Big\} \\ -----------------\)
11. \(2(5x^2+5x)=-(-3x^2-7x) \\ \Leftrightarrow 10x^2+10x=3x^2+7x \\ \Leftrightarrow 10x^2+10x-3x^2-7x= 0 \\ \Leftrightarrow 7x^2-3x=0 \\ \Leftrightarrow x(7x-3) = 0 \\ \Leftrightarrow x = 0 \vee 7x-3=0 \\ \Leftrightarrow x = 0 \vee x = \frac{3}{7} \\ V = \Big\{ \frac{3}{7}; 0 \Big\} \\ -----------------\)
12. \(2x^2+6x=4x^2-7x \\ \Leftrightarrow -2x^2+13x=0 \\ \Leftrightarrow x(-2x+13) = 0 \\ \Leftrightarrow x = 0 \vee -2x+13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-13}{-2} = \frac{13}{2} \\ V = \Big\{ \frac{13}{2}; 0 \Big\} \\ -----------------\)