Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-13x^2+7x=-5x^2+8x\)
2. \(-6x^2+5x=-5x^2+5x\)
3. \(3(-3x^2+6x)=-(2x^2-17x)\)
4. \(-12x^2-26x=-9x^2-7x\)
5. \(8x^2+24x=2x^2+6x\)
6. \(x^2+10x=-4x^2+4x\)
7. \(5x^2+5x=0\)
8. \(5(7x^2+4x)=-(-39x^2-35x)\)
9. \(-2(8x^2+8x)=-(18x^2+6x)\)
10. \(3x^2+14x=4x^2+6x\)
11. \(-9x^2+x=-6x^2-3x\)
12. \(-7x^2-3x=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-13x^2+7x=-5x^2+8x \\ \Leftrightarrow -8x^2-1x=0 \\ \Leftrightarrow x(-8x-1) = 0 \\ \Leftrightarrow x = 0 \vee -8x-1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{1}{-8} = \frac{-1}{8} \\ V = \Big\{ 0 ; \frac{-1}{8} \Big\} \\ -----------------\)
2. \(-6x^2+5x=-5x^2+5x \\ \Leftrightarrow -x^2+0x=0 \\ \Leftrightarrow -x^2=0 \\ \Leftrightarrow x^2 = \frac{0}{-1} \\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
3. \(3(-3x^2+6x)=-(2x^2-17x) \\ \Leftrightarrow -9x^2+18x=-2x^2+17x \\ \Leftrightarrow -9x^2+18x+2x^2-17x= 0 \\ \Leftrightarrow -7x^2-1x=0 \\ \Leftrightarrow x(-7x-1) = 0 \\ \Leftrightarrow x = 0 \vee -7x-1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{1}{-7} = \frac{-1}{7} \\ V = \Big\{ 0 ; \frac{-1}{7} \Big\} \\ -----------------\)
4. \(-12x^2-26x=-9x^2-7x \\ \Leftrightarrow -3x^2-19x=0 \\ \Leftrightarrow x(-3x-19) = 0 \\ \Leftrightarrow x = 0 \vee -3x-19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{19}{-3} = \frac{-19}{3} \\ V = \Big\{ 0 ; \frac{-19}{3} \Big\} \\ -----------------\)
5. \(8x^2+24x=2x^2+6x \\ \Leftrightarrow 6x^2+18x=0 \\ \Leftrightarrow x(6x+18) = 0 \\ \Leftrightarrow x = 0 \vee 6x+18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-18}{6} = -3 \\ V = \Big\{ 0 ; -3 \Big\} \\ -----------------\)
6. \(x^2+10x=-4x^2+4x \\ \Leftrightarrow 5x^2+6x=0 \\ \Leftrightarrow x(5x+6) = 0 \\ \Leftrightarrow x = 0 \vee 5x+6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-6}{5} \\ V = \Big\{ 0 ; \frac{-6}{5} \Big\} \\ -----------------\)
7. \(5x^2+5x=0 \\ \Leftrightarrow x(5x+5) = 0 \\ \Leftrightarrow x = 0 \vee 5x+5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-5}{5} = -1 \\ V = \Big\{ 0 ; -1 \Big\} \\ -----------------\)
8. \(5(7x^2+4x)=-(-39x^2-35x) \\ \Leftrightarrow 35x^2+20x=39x^2+35x \\ \Leftrightarrow 35x^2+20x-39x^2-35x= 0 \\ \Leftrightarrow -4x^2+15x=0 \\ \Leftrightarrow x(-4x+15) = 0 \\ \Leftrightarrow x = 0 \vee -4x+15=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-15}{-4} = \frac{15}{4} \\ V = \Big\{ \frac{15}{4}; 0 \Big\} \\ -----------------\)
9. \(-2(8x^2+8x)=-(18x^2+6x) \\ \Leftrightarrow -16x^2-16x=-18x^2-6x \\ \Leftrightarrow -16x^2-16x+18x^2+6x= 0 \\ \Leftrightarrow 2x^2+10x=0 \\ \Leftrightarrow x(2x+10) = 0 \\ \Leftrightarrow x = 0 \vee 2x+10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-10}{2} = -5 \\ V = \Big\{ 0 ; -5 \Big\} \\ -----------------\)
10. \(3x^2+14x=4x^2+6x \\ \Leftrightarrow -x^2+8x=0 \\ \Leftrightarrow x(-x+8) = 0 \\ \Leftrightarrow x = 0 \vee -x+8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-8}{-1} = 8 \\ V = \Big\{ 8; 0 \Big\} \\ -----------------\)
11. \(-9x^2+x=-6x^2-3x \\ \Leftrightarrow -3x^2+4x=0 \\ \Leftrightarrow x(-3x+4) = 0 \\ \Leftrightarrow x = 0 \vee -3x+4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-4}{-3} = \frac{4}{3} \\ V = \Big\{ \frac{4}{3}; 0 \Big\} \\ -----------------\)
12. \(-7x^2-3x=0 \\ \Leftrightarrow x(-7x-3) = 0 \\ \Leftrightarrow x = 0 \vee -7x-3=0 \\ \Leftrightarrow x = 0 \vee x = \frac{3}{-7} = \frac{-3}{7} \\ V = \Big\{ 0 ; \frac{-3}{7} \Big\} \\ -----------------\)