Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-8x^2-7x=0\)
2. \(-5x^2+22x=0\)
3. \(-9x^2-6x=-5x^2-4x\)
4. \(4(10x^2-8x)=-(-41x^2+47x)\)
5. \(-3x^2+24x=0\)
6. \(3(-2x^2+6x)=-(x^2-21x)\)
7. \(-5x^2+18x=-7x^2+3x\)
8. \(3x^2+27x=7x^2+8x\)
9. \(7x^2-18x=0\)
10. \(4x^2+32x=6x^2+10x\)
11. \(-10x^2+5x=-9x^2+10x\)
12. \(2(3x^2+9x)=-(-2x^2-32x)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-8x^2-7x=0 \\ \Leftrightarrow x(-8x-7) = 0 \\ \Leftrightarrow x = 0 \vee -8x-7=0 \\ \Leftrightarrow x = 0 \vee x = \frac{7}{-8} = \frac{-7}{8} \\ V = \Big\{ 0 ; \frac{-7}{8} \Big\} \\ -----------------\)
2. \(-5x^2+22x=0 \\ \Leftrightarrow x(-5x+22) = 0 \\ \Leftrightarrow x = 0 \vee -5x+22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-22}{-5} = \frac{22}{5} \\ V = \Big\{ \frac{22}{5}; 0 \Big\} \\ -----------------\)
3. \(-9x^2-6x=-5x^2-4x \\ \Leftrightarrow -4x^2-2x=0 \\ \Leftrightarrow x(-4x-2) = 0 \\ \Leftrightarrow x = 0 \vee -4x-2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{2}{-4} = \frac{-1}{2} \\ V = \Big\{ 0 ; \frac{-1}{2} \Big\} \\ -----------------\)
4. \(4(10x^2-8x)=-(-41x^2+47x) \\ \Leftrightarrow 40x^2-32x=41x^2-47x \\ \Leftrightarrow 40x^2-32x-41x^2+47x= 0 \\ \Leftrightarrow -x^2-15x=0 \\ \Leftrightarrow x(-x-15) = 0 \\ \Leftrightarrow x = 0 \vee -x-15=0 \\ \Leftrightarrow x = 0 \vee x = \frac{15}{-1} = -15 \\ V = \Big\{ 0 ; -15 \Big\} \\ -----------------\)
5. \(-3x^2+24x=0 \\ \Leftrightarrow x(-3x+24) = 0 \\ \Leftrightarrow x = 0 \vee -3x+24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-24}{-3} = 8 \\ V = \Big\{ 8; 0 \Big\} \\ -----------------\)
6. \(3(-2x^2+6x)=-(x^2-21x) \\ \Leftrightarrow -6x^2+18x=-x^2+21x \\ \Leftrightarrow -6x^2+18x+x^2-21x= 0 \\ \Leftrightarrow -5x^2+3x=0 \\ \Leftrightarrow x(-5x+3) = 0 \\ \Leftrightarrow x = 0 \vee -5x+3=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-3}{-5} = \frac{3}{5} \\ V = \Big\{ \frac{3}{5}; 0 \Big\} \\ -----------------\)
7. \(-5x^2+18x=-7x^2+3x \\ \Leftrightarrow 2x^2+15x=0 \\ \Leftrightarrow x(2x+15) = 0 \\ \Leftrightarrow x = 0 \vee 2x+15=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-15}{2} \\ V = \Big\{ 0 ; \frac{-15}{2} \Big\} \\ -----------------\)
8. \(3x^2+27x=7x^2+8x \\ \Leftrightarrow -4x^2+19x=0 \\ \Leftrightarrow x(-4x+19) = 0 \\ \Leftrightarrow x = 0 \vee -4x+19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-19}{-4} = \frac{19}{4} \\ V = \Big\{ \frac{19}{4}; 0 \Big\} \\ -----------------\)
9. \(7x^2-18x=0 \\ \Leftrightarrow x(7x-18) = 0 \\ \Leftrightarrow x = 0 \vee 7x-18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{18}{7} \\ V = \Big\{ \frac{18}{7}; 0 \Big\} \\ -----------------\)
10. \(4x^2+32x=6x^2+10x \\ \Leftrightarrow -2x^2+22x=0 \\ \Leftrightarrow x(-2x+22) = 0 \\ \Leftrightarrow x = 0 \vee -2x+22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-22}{-2} = 11 \\ V = \Big\{ 11; 0 \Big\} \\ -----------------\)
11. \(-10x^2+5x=-9x^2+10x \\ \Leftrightarrow -x^2-5x=0 \\ \Leftrightarrow x(-x-5) = 0 \\ \Leftrightarrow x = 0 \vee -x-5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{5}{-1} = -5 \\ V = \Big\{ 0 ; -5 \Big\} \\ -----------------\)
12. \(2(3x^2+9x)=-(-2x^2-32x) \\ \Leftrightarrow 6x^2+18x=2x^2+32x \\ \Leftrightarrow 6x^2+18x-2x^2-32x= 0 \\ \Leftrightarrow 4x^2+14x=0 \\ \Leftrightarrow x(4x+14) = 0 \\ \Leftrightarrow x = 0 \vee 4x+14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-14}{4} = \frac{-7}{2} \\ V = \Big\{ 0 ; \frac{-7}{2} \Big\} \\ -----------------\)