Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-14x^2-4x=-6x^2+4x\)
2. \(-2x^2-6x=4x^2-8x\)
3. \(-x^2+21x=-3x^2+5x\)
4. \(5(2x^2+7x)=-(-6x^2-12x)\)
5. \(15x^2+6x=7x^2-3x\)
6. \(-4(8x^2+3x)=-(29x^2-2x)\)
7. \(6x^2-22x=0\)
8. \(3(-9x^2-9x)=-(30x^2+35x)\)
9. \(2(2x^2+5x)=-(-8x^2-31x)\)
10. \(-4x^2+10x=0\)
11. \(x^2+x=6x^2+4x\)
12. \(-3(-9x^2+2x)=-(-23x^2+24x)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-14x^2-4x=-6x^2+4x \\ \Leftrightarrow -8x^2-8x=0 \\ \Leftrightarrow x(-8x-8) = 0 \\ \Leftrightarrow x = 0 \vee -8x-8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{8}{-8} = -1 \\ V = \Big\{ 0 ; -1 \Big\} \\ -----------------\)
2. \(-2x^2-6x=4x^2-8x \\ \Leftrightarrow -6x^2+2x=0 \\ \Leftrightarrow x(-6x+2) = 0 \\ \Leftrightarrow x = 0 \vee -6x+2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-2}{-6} = \frac{1}{3} \\ V = \Big\{ \frac{1}{3}; 0 \Big\} \\ -----------------\)
3. \(-x^2+21x=-3x^2+5x \\ \Leftrightarrow 2x^2+16x=0 \\ \Leftrightarrow x(2x+16) = 0 \\ \Leftrightarrow x = 0 \vee 2x+16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-16}{2} = -8 \\ V = \Big\{ 0 ; -8 \Big\} \\ -----------------\)
4. \(5(2x^2+7x)=-(-6x^2-12x) \\ \Leftrightarrow 10x^2+35x=6x^2+12x \\ \Leftrightarrow 10x^2+35x-6x^2-12x= 0 \\ \Leftrightarrow 4x^2-23x=0 \\ \Leftrightarrow x(4x-23) = 0 \\ \Leftrightarrow x = 0 \vee 4x-23=0 \\ \Leftrightarrow x = 0 \vee x = \frac{23}{4} \\ V = \Big\{ \frac{23}{4}; 0 \Big\} \\ -----------------\)
5. \(15x^2+6x=7x^2-3x \\ \Leftrightarrow 8x^2+9x=0 \\ \Leftrightarrow x(8x+9) = 0 \\ \Leftrightarrow x = 0 \vee 8x+9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-9}{8} \\ V = \Big\{ 0 ; \frac{-9}{8} \Big\} \\ -----------------\)
6. \(-4(8x^2+3x)=-(29x^2-2x) \\ \Leftrightarrow -32x^2-12x=-29x^2+2x \\ \Leftrightarrow -32x^2-12x+29x^2-2x= 0 \\ \Leftrightarrow -3x^2+14x=0 \\ \Leftrightarrow x(-3x+14) = 0 \\ \Leftrightarrow x = 0 \vee -3x+14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-14}{-3} = \frac{14}{3} \\ V = \Big\{ \frac{14}{3}; 0 \Big\} \\ -----------------\)
7. \(6x^2-22x=0 \\ \Leftrightarrow x(6x-22) = 0 \\ \Leftrightarrow x = 0 \vee 6x-22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{22}{6} = \frac{11}{3} \\ V = \Big\{ \frac{11}{3}; 0 \Big\} \\ -----------------\)
8. \(3(-9x^2-9x)=-(30x^2+35x) \\ \Leftrightarrow -27x^2-27x=-30x^2-35x \\ \Leftrightarrow -27x^2-27x+30x^2+35x= 0 \\ \Leftrightarrow 3x^2-8x=0 \\ \Leftrightarrow x(3x-8) = 0 \\ \Leftrightarrow x = 0 \vee 3x-8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{8}{3} \\ V = \Big\{ \frac{8}{3}; 0 \Big\} \\ -----------------\)
9. \(2(2x^2+5x)=-(-8x^2-31x) \\ \Leftrightarrow 4x^2+10x=8x^2+31x \\ \Leftrightarrow 4x^2+10x-8x^2-31x= 0 \\ \Leftrightarrow -4x^2+21x=0 \\ \Leftrightarrow x(-4x+21) = 0 \\ \Leftrightarrow x = 0 \vee -4x+21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-21}{-4} = \frac{21}{4} \\ V = \Big\{ \frac{21}{4}; 0 \Big\} \\ -----------------\)
10. \(-4x^2+10x=0 \\ \Leftrightarrow x(-4x+10) = 0 \\ \Leftrightarrow x = 0 \vee -4x+10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-10}{-4} = \frac{5}{2} \\ V = \Big\{ \frac{5}{2}; 0 \Big\} \\ -----------------\)
11. \(x^2+x=6x^2+4x \\ \Leftrightarrow -5x^2-3x=0 \\ \Leftrightarrow x(-5x-3) = 0 \\ \Leftrightarrow x = 0 \vee -5x-3=0 \\ \Leftrightarrow x = 0 \vee x = \frac{3}{-5} = \frac{-3}{5} \\ V = \Big\{ 0 ; \frac{-3}{5} \Big\} \\ -----------------\)
12. \(-3(-9x^2+2x)=-(-23x^2+24x) \\ \Leftrightarrow 27x^2-6x=23x^2-24x \\ \Leftrightarrow 27x^2-6x-23x^2+24x= 0 \\ \Leftrightarrow 4x^2-18x=0 \\ \Leftrightarrow x(4x-18) = 0 \\ \Leftrightarrow x = 0 \vee 4x-18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{18}{4} = \frac{9}{2} \\ V = \Big\{ \frac{9}{2}; 0 \Big\} \\ -----------------\)