Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(4(7x^2-6x)=-(-36x^2+25x)\)
2. \(2(-9x^2+2x)=-(17x^2-12x)\)
3. \(2x^2-25x=8x^2-9x\)
4. \(-5(4x^2-5x)=-(12x^2-6x)\)
5. \(-4x^2-24x=0\)
6. \(4x^2-7x=0\)
7. \(17x^2+11x=10x^2+2x\)
8. \(-7x^2+12x=-10x^2+8x\)
9. \(-3(-7x^2+10x)=-(-19x^2+11x)\)
10. \(-4(-4x^2+4x)=-(-11x^2-8x)\)
11. \(-2x^2+10x=-6x^2+8x\)
12. \(-6x^2+1x=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(4(7x^2-6x)=-(-36x^2+25x) \\ \Leftrightarrow 28x^2-24x=36x^2-25x \\ \Leftrightarrow 28x^2-24x-36x^2+25x= 0 \\ \Leftrightarrow -8x^2-1x=0 \\ \Leftrightarrow x(-8x-1) = 0 \\ \Leftrightarrow x = 0 \vee -8x-1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{1}{-8} = \frac{-1}{8} \\ V = \Big\{ 0 ; \frac{-1}{8} \Big\} \\ -----------------\)
2. \(2(-9x^2+2x)=-(17x^2-12x) \\ \Leftrightarrow -18x^2+4x=-17x^2+12x \\ \Leftrightarrow -18x^2+4x+17x^2-12x= 0 \\ \Leftrightarrow -x^2+8x=0 \\ \Leftrightarrow x(-x+8) = 0 \\ \Leftrightarrow x = 0 \vee -x+8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-8}{-1} = 8 \\ V = \Big\{ 8; 0 \Big\} \\ -----------------\)
3. \(2x^2-25x=8x^2-9x \\ \Leftrightarrow -6x^2-16x=0 \\ \Leftrightarrow x(-6x-16) = 0 \\ \Leftrightarrow x = 0 \vee -6x-16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{16}{-6} = \frac{-8}{3} \\ V = \Big\{ 0 ; \frac{-8}{3} \Big\} \\ -----------------\)
4. \(-5(4x^2-5x)=-(12x^2-6x) \\ \Leftrightarrow -20x^2+25x=-12x^2+6x \\ \Leftrightarrow -20x^2+25x+12x^2-6x= 0 \\ \Leftrightarrow -8x^2-19x=0 \\ \Leftrightarrow x(-8x-19) = 0 \\ \Leftrightarrow x = 0 \vee -8x-19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{19}{-8} = \frac{-19}{8} \\ V = \Big\{ 0 ; \frac{-19}{8} \Big\} \\ -----------------\)
5. \(-4x^2-24x=0 \\ \Leftrightarrow x(-4x-24) = 0 \\ \Leftrightarrow x = 0 \vee -4x-24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{24}{-4} = -6 \\ V = \Big\{ 0 ; -6 \Big\} \\ -----------------\)
6. \(4x^2-7x=0 \\ \Leftrightarrow x(4x-7) = 0 \\ \Leftrightarrow x = 0 \vee 4x-7=0 \\ \Leftrightarrow x = 0 \vee x = \frac{7}{4} \\ V = \Big\{ \frac{7}{4}; 0 \Big\} \\ -----------------\)
7. \(17x^2+11x=10x^2+2x \\ \Leftrightarrow 7x^2+9x=0 \\ \Leftrightarrow x(7x+9) = 0 \\ \Leftrightarrow x = 0 \vee 7x+9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-9}{7} \\ V = \Big\{ 0 ; \frac{-9}{7} \Big\} \\ -----------------\)
8. \(-7x^2+12x=-10x^2+8x \\ \Leftrightarrow 3x^2+4x=0 \\ \Leftrightarrow x(3x+4) = 0 \\ \Leftrightarrow x = 0 \vee 3x+4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-4}{3} \\ V = \Big\{ 0 ; \frac{-4}{3} \Big\} \\ -----------------\)
9. \(-3(-7x^2+10x)=-(-19x^2+11x) \\ \Leftrightarrow 21x^2-30x=19x^2-11x \\ \Leftrightarrow 21x^2-30x-19x^2+11x= 0 \\ \Leftrightarrow 2x^2+19x=0 \\ \Leftrightarrow x(2x+19) = 0 \\ \Leftrightarrow x = 0 \vee 2x+19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-19}{2} \\ V = \Big\{ 0 ; \frac{-19}{2} \Big\} \\ -----------------\)
10. \(-4(-4x^2+4x)=-(-11x^2-8x) \\ \Leftrightarrow 16x^2-16x=11x^2+8x \\ \Leftrightarrow 16x^2-16x-11x^2-8x= 0 \\ \Leftrightarrow 5x^2+24x=0 \\ \Leftrightarrow x(5x+24) = 0 \\ \Leftrightarrow x = 0 \vee 5x+24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-24}{5} \\ V = \Big\{ 0 ; \frac{-24}{5} \Big\} \\ -----------------\)
11. \(-2x^2+10x=-6x^2+8x \\ \Leftrightarrow 4x^2+2x=0 \\ \Leftrightarrow x(4x+2) = 0 \\ \Leftrightarrow x = 0 \vee 4x+2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-2}{4} = \frac{-1}{2} \\ V = \Big\{ 0 ; \frac{-1}{2} \Big\} \\ -----------------\)
12. \(-6x^2+1x=0 \\ \Leftrightarrow x(-6x+1) = 0 \\ \Leftrightarrow x = 0 \vee -6x+1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-1}{-6} = \frac{1}{6} \\ V = \Big\{ \frac{1}{6}; 0 \Big\} \\ -----------------\)