Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(4(-6x^2-3x)=-(22x^2+22x)\)
2. \(-4x^2-31x=3x^2-7x\)
3. \(3x^2-18x=0\)
4. \(3(6x^2+7x)=-(-20x^2-13x)\)
5. \(-4(2x^2-5x)=-(11x^2-40x)\)
6. \(-4x^2-11x=4x^2-5x\)
7. \(-3(9x^2+10x)=-(26x^2+25x)\)
8. \(-4x^2-4x=-7x^2-3x\)
9. \(-2(8x^2-5x)=-(20x^2-24x)\)
10. \(-3(-3x^2+10x)=-(-16x^2+55x)\)
11. \(-5x^2-1x=0\)
12. \(15x^2-16x=10x^2+5x\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(4(-6x^2-3x)=-(22x^2+22x) \\ \Leftrightarrow -24x^2-12x=-22x^2-22x \\ \Leftrightarrow -24x^2-12x+22x^2+22x= 0 \\ \Leftrightarrow -2x^2-10x=0 \\ \Leftrightarrow x(-2x-10) = 0 \\ \Leftrightarrow x = 0 \vee -2x-10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{10}{-2} = -5 \\ V = \Big\{ 0 ; -5 \Big\} \\ -----------------\)
2. \(-4x^2-31x=3x^2-7x \\ \Leftrightarrow -7x^2-24x=0 \\ \Leftrightarrow x(-7x-24) = 0 \\ \Leftrightarrow x = 0 \vee -7x-24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{24}{-7} = \frac{-24}{7} \\ V = \Big\{ 0 ; \frac{-24}{7} \Big\} \\ -----------------\)
3. \(3x^2-18x=0 \\ \Leftrightarrow x(3x-18) = 0 \\ \Leftrightarrow x = 0 \vee 3x-18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{18}{3} = 6 \\ V = \Big\{ 6; 0 \Big\} \\ -----------------\)
4. \(3(6x^2+7x)=-(-20x^2-13x) \\ \Leftrightarrow 18x^2+21x=20x^2+13x \\ \Leftrightarrow 18x^2+21x-20x^2-13x= 0 \\ \Leftrightarrow -2x^2-8x=0 \\ \Leftrightarrow x(-2x-8) = 0 \\ \Leftrightarrow x = 0 \vee -2x-8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{8}{-2} = -4 \\ V = \Big\{ 0 ; -4 \Big\} \\ -----------------\)
5. \(-4(2x^2-5x)=-(11x^2-40x) \\ \Leftrightarrow -8x^2+20x=-11x^2+40x \\ \Leftrightarrow -8x^2+20x+11x^2-40x= 0 \\ \Leftrightarrow 3x^2+20x=0 \\ \Leftrightarrow x(3x+20) = 0 \\ \Leftrightarrow x = 0 \vee 3x+20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-20}{3} \\ V = \Big\{ 0 ; \frac{-20}{3} \Big\} \\ -----------------\)
6. \(-4x^2-11x=4x^2-5x \\ \Leftrightarrow -8x^2-6x=0 \\ \Leftrightarrow x(-8x-6) = 0 \\ \Leftrightarrow x = 0 \vee -8x-6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{6}{-8} = \frac{-3}{4} \\ V = \Big\{ 0 ; \frac{-3}{4} \Big\} \\ -----------------\)
7. \(-3(9x^2+10x)=-(26x^2+25x) \\ \Leftrightarrow -27x^2-30x=-26x^2-25x \\ \Leftrightarrow -27x^2-30x+26x^2+25x= 0 \\ \Leftrightarrow -x^2+5x=0 \\ \Leftrightarrow x(-x+5) = 0 \\ \Leftrightarrow x = 0 \vee -x+5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-5}{-1} = 5 \\ V = \Big\{ 5; 0 \Big\} \\ -----------------\)
8. \(-4x^2-4x=-7x^2-3x \\ \Leftrightarrow 3x^2-1x=0 \\ \Leftrightarrow x(3x-1) = 0 \\ \Leftrightarrow x = 0 \vee 3x-1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{1}{3} \\ V = \Big\{ \frac{1}{3}; 0 \Big\} \\ -----------------\)
9. \(-2(8x^2-5x)=-(20x^2-24x) \\ \Leftrightarrow -16x^2+10x=-20x^2+24x \\ \Leftrightarrow -16x^2+10x+20x^2-24x= 0 \\ \Leftrightarrow 4x^2+14x=0 \\ \Leftrightarrow x(4x+14) = 0 \\ \Leftrightarrow x = 0 \vee 4x+14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-14}{4} = \frac{-7}{2} \\ V = \Big\{ 0 ; \frac{-7}{2} \Big\} \\ -----------------\)
10. \(-3(-3x^2+10x)=-(-16x^2+55x) \\ \Leftrightarrow 9x^2-30x=16x^2-55x \\ \Leftrightarrow 9x^2-30x-16x^2+55x= 0 \\ \Leftrightarrow -7x^2-25x=0 \\ \Leftrightarrow x(-7x-25) = 0 \\ \Leftrightarrow x = 0 \vee -7x-25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{25}{-7} = \frac{-25}{7} \\ V = \Big\{ 0 ; \frac{-25}{7} \Big\} \\ -----------------\)
11. \(-5x^2-1x=0 \\ \Leftrightarrow x(-5x-1) = 0 \\ \Leftrightarrow x = 0 \vee -5x-1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{1}{-5} = \frac{-1}{5} \\ V = \Big\{ 0 ; \frac{-1}{5} \Big\} \\ -----------------\)
12. \(15x^2-16x=10x^2+5x \\ \Leftrightarrow 5x^2-21x=0 \\ \Leftrightarrow x(5x-21) = 0 \\ \Leftrightarrow x = 0 \vee 5x-21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{21}{5} \\ V = \Big\{ \frac{21}{5}; 0 \Big\} \\ -----------------\)