Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(5(-7x^2-4x)=-(33x^2+12x)\)
2. \(-8x^2+26x=-7x^2+5x\)
3. \(4x^2+4x=0\)
4. \(-12x^2-19x=-5x^2-4x\)
5. \(9x^2+18x=10x^2-4x\)
6. \(3(-5x^2-6x)=-(22x^2+40x)\)
7. \(-3x^2+11x=0\)
8. \(x^2+7x=-2x^2+10x\)
9. \(-3(3x^2-9x)=-(3x^2-5x)\)
10. \(-8x^2-23x=0\)
11. \(-9x^2-x=-6x^2+3x\)
12. \(2(-4x^2+2x)=-(11x^2-19x)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(5(-7x^2-4x)=-(33x^2+12x) \\ \Leftrightarrow -35x^2-20x=-33x^2-12x \\ \Leftrightarrow -35x^2-20x+33x^2+12x= 0 \\ \Leftrightarrow -2x^2+8x=0 \\ \Leftrightarrow x(-2x+8) = 0 \\ \Leftrightarrow x = 0 \vee -2x+8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-8}{-2} = 4 \\ V = \Big\{ 4; 0 \Big\} \\ -----------------\)
2. \(-8x^2+26x=-7x^2+5x \\ \Leftrightarrow -x^2+21x=0 \\ \Leftrightarrow x(-x+21) = 0 \\ \Leftrightarrow x = 0 \vee -x+21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-21}{-1} = 21 \\ V = \Big\{ 21; 0 \Big\} \\ -----------------\)
3. \(4x^2+4x=0 \\ \Leftrightarrow x(4x+4) = 0 \\ \Leftrightarrow x = 0 \vee 4x+4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-4}{4} = -1 \\ V = \Big\{ 0 ; -1 \Big\} \\ -----------------\)
4. \(-12x^2-19x=-5x^2-4x \\ \Leftrightarrow -7x^2-15x=0 \\ \Leftrightarrow x(-7x-15) = 0 \\ \Leftrightarrow x = 0 \vee -7x-15=0 \\ \Leftrightarrow x = 0 \vee x = \frac{15}{-7} = \frac{-15}{7} \\ V = \Big\{ 0 ; \frac{-15}{7} \Big\} \\ -----------------\)
5. \(9x^2+18x=10x^2-4x \\ \Leftrightarrow -x^2+22x=0 \\ \Leftrightarrow x(-x+22) = 0 \\ \Leftrightarrow x = 0 \vee -x+22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-22}{-1} = 22 \\ V = \Big\{ 22; 0 \Big\} \\ -----------------\)
6. \(3(-5x^2-6x)=-(22x^2+40x) \\ \Leftrightarrow -15x^2-18x=-22x^2-40x \\ \Leftrightarrow -15x^2-18x+22x^2+40x= 0 \\ \Leftrightarrow 7x^2-22x=0 \\ \Leftrightarrow x(7x-22) = 0 \\ \Leftrightarrow x = 0 \vee 7x-22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{22}{7} \\ V = \Big\{ \frac{22}{7}; 0 \Big\} \\ -----------------\)
7. \(-3x^2+11x=0 \\ \Leftrightarrow x(-3x+11) = 0 \\ \Leftrightarrow x = 0 \vee -3x+11=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-11}{-3} = \frac{11}{3} \\ V = \Big\{ \frac{11}{3}; 0 \Big\} \\ -----------------\)
8. \(x^2+7x=-2x^2+10x \\ \Leftrightarrow 3x^2-3x=0 \\ \Leftrightarrow x(3x-3) = 0 \\ \Leftrightarrow x = 0 \vee 3x-3=0 \\ \Leftrightarrow x = 0 \vee x = \frac{3}{3} = 1 \\ V = \Big\{ 1; 0 \Big\} \\ -----------------\)
9. \(-3(3x^2-9x)=-(3x^2-5x) \\ \Leftrightarrow -9x^2+27x=-3x^2+5x \\ \Leftrightarrow -9x^2+27x+3x^2-5x= 0 \\ \Leftrightarrow -6x^2-22x=0 \\ \Leftrightarrow x(-6x-22) = 0 \\ \Leftrightarrow x = 0 \vee -6x-22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{22}{-6} = \frac{-11}{3} \\ V = \Big\{ 0 ; \frac{-11}{3} \Big\} \\ -----------------\)
10. \(-8x^2-23x=0 \\ \Leftrightarrow x(-8x-23) = 0 \\ \Leftrightarrow x = 0 \vee -8x-23=0 \\ \Leftrightarrow x = 0 \vee x = \frac{23}{-8} = \frac{-23}{8} \\ V = \Big\{ 0 ; \frac{-23}{8} \Big\} \\ -----------------\)
11. \(-9x^2-x=-6x^2+3x \\ \Leftrightarrow -3x^2-4x=0 \\ \Leftrightarrow x(-3x-4) = 0 \\ \Leftrightarrow x = 0 \vee -3x-4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{4}{-3} = \frac{-4}{3} \\ V = \Big\{ 0 ; \frac{-4}{3} \Big\} \\ -----------------\)
12. \(2(-4x^2+2x)=-(11x^2-19x) \\ \Leftrightarrow -8x^2+4x=-11x^2+19x \\ \Leftrightarrow -8x^2+4x+11x^2-19x= 0 \\ \Leftrightarrow 3x^2+15x=0 \\ \Leftrightarrow x(3x+15) = 0 \\ \Leftrightarrow x = 0 \vee 3x+15=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-15}{3} = -5 \\ V = \Big\{ 0 ; -5 \Big\} \\ -----------------\)