Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(2(-8x^2-4x)=-(17x^2-10x)\)
2. \(-x^2+21x=0\)
3. \(2(5x^2-8x)=-(-8x^2+0x)\)
4. \(-5x^2-31x=-4x^2-9x\)
5. \(4(3x^2+3x)=-(-17x^2-34x)\)
6. \(3x^2+28x=8x^2+10x\)
7. \(3x^2-21x=-4x^2-9x\)
8. \(-2x^2+22x=0\)
9. \(2(-7x^2+6x)=-(10x^2-17x)\)
10. \(-5(5x^2-5x)=-(29x^2-39x)\)
11. \(6x^2-19x=0\)
12. \(x^2-7x=2x^2-7x\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(2(-8x^2-4x)=-(17x^2-10x) \\ \Leftrightarrow -16x^2-8x=-17x^2+10x \\ \Leftrightarrow -16x^2-8x+17x^2-10x= 0 \\ \Leftrightarrow x^2+18x=0 \\ \Leftrightarrow x(x+18) = 0 \\ \Leftrightarrow x = 0 \vee x+18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-18}{1} = -18 \\ V = \Big\{ 0 ; -18 \Big\} \\ -----------------\)
2. \(-x^2+21x=0 \\ \Leftrightarrow x(-x+21) = 0 \\ \Leftrightarrow x = 0 \vee -x+21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-21}{-1} = 21 \\ V = \Big\{ 21; 0 \Big\} \\ -----------------\)
3. \(2(5x^2-8x)=-(-8x^2+0x) \\ \Leftrightarrow 10x^2-16x=8x^2+0x \\ \Leftrightarrow 10x^2-16x-8x^2+0x= 0 \\ \Leftrightarrow 2x^2+16x=0 \\ \Leftrightarrow x(2x+16) = 0 \\ \Leftrightarrow x = 0 \vee 2x+16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-16}{2} = -8 \\ V = \Big\{ 0 ; -8 \Big\} \\ -----------------\)
4. \(-5x^2-31x=-4x^2-9x \\ \Leftrightarrow -x^2-22x=0 \\ \Leftrightarrow x(-x-22) = 0 \\ \Leftrightarrow x = 0 \vee -x-22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{22}{-1} = -22 \\ V = \Big\{ 0 ; -22 \Big\} \\ -----------------\)
5. \(4(3x^2+3x)=-(-17x^2-34x) \\ \Leftrightarrow 12x^2+12x=17x^2+34x \\ \Leftrightarrow 12x^2+12x-17x^2-34x= 0 \\ \Leftrightarrow -5x^2+22x=0 \\ \Leftrightarrow x(-5x+22) = 0 \\ \Leftrightarrow x = 0 \vee -5x+22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-22}{-5} = \frac{22}{5} \\ V = \Big\{ \frac{22}{5}; 0 \Big\} \\ -----------------\)
6. \(3x^2+28x=8x^2+10x \\ \Leftrightarrow -5x^2+18x=0 \\ \Leftrightarrow x(-5x+18) = 0 \\ \Leftrightarrow x = 0 \vee -5x+18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-18}{-5} = \frac{18}{5} \\ V = \Big\{ \frac{18}{5}; 0 \Big\} \\ -----------------\)
7. \(3x^2-21x=-4x^2-9x \\ \Leftrightarrow 7x^2-12x=0 \\ \Leftrightarrow x(7x-12) = 0 \\ \Leftrightarrow x = 0 \vee 7x-12=0 \\ \Leftrightarrow x = 0 \vee x = \frac{12}{7} \\ V = \Big\{ \frac{12}{7}; 0 \Big\} \\ -----------------\)
8. \(-2x^2+22x=0 \\ \Leftrightarrow x(-2x+22) = 0 \\ \Leftrightarrow x = 0 \vee -2x+22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-22}{-2} = 11 \\ V = \Big\{ 11; 0 \Big\} \\ -----------------\)
9. \(2(-7x^2+6x)=-(10x^2-17x) \\ \Leftrightarrow -14x^2+12x=-10x^2+17x \\ \Leftrightarrow -14x^2+12x+10x^2-17x= 0 \\ \Leftrightarrow -4x^2+5x=0 \\ \Leftrightarrow x(-4x+5) = 0 \\ \Leftrightarrow x = 0 \vee -4x+5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-5}{-4} = \frac{5}{4} \\ V = \Big\{ \frac{5}{4}; 0 \Big\} \\ -----------------\)
10. \(-5(5x^2-5x)=-(29x^2-39x) \\ \Leftrightarrow -25x^2+25x=-29x^2+39x \\ \Leftrightarrow -25x^2+25x+29x^2-39x= 0 \\ \Leftrightarrow 4x^2+14x=0 \\ \Leftrightarrow x(4x+14) = 0 \\ \Leftrightarrow x = 0 \vee 4x+14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-14}{4} = \frac{-7}{2} \\ V = \Big\{ 0 ; \frac{-7}{2} \Big\} \\ -----------------\)
11. \(6x^2-19x=0 \\ \Leftrightarrow x(6x-19) = 0 \\ \Leftrightarrow x = 0 \vee 6x-19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{19}{6} \\ V = \Big\{ \frac{19}{6}; 0 \Big\} \\ -----------------\)
12. \(x^2-7x=2x^2-7x \\ \Leftrightarrow -x^2+0x=0 \\ \Leftrightarrow -x^2=0 \\ \Leftrightarrow x^2 = \frac{0}{-1} \\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)