Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-6x^2+22x=0\)
2. \(-2(2x^2+4x)=-(-3x^2-11x)\)
3. \(2(-8x^2+8x)=-(15x^2+2x)\)
4. \(-3(-9x^2+5x)=-(-30x^2+31x)\)
5. \(-7x^2-16x=0\)
6. \(x^2-10x=0\)
7. \(4(7x^2-2x)=-(-26x^2-4x)\)
8. \(-8x^2+5x=0\)
9. \(-4(-2x^2+8x)=-(-16x^2+9x)\)
10. \(-5x^2-21x=0\)
11. \(-5x^2+7x=-2x^2-10x\)
12. \(-4x^2-15x=-3x^2+8x\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-6x^2+22x=0 \\ \Leftrightarrow x(-6x+22) = 0 \\ \Leftrightarrow x = 0 \vee -6x+22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-22}{-6} = \frac{11}{3} \\ V = \Big\{ \frac{11}{3}; 0 \Big\} \\ -----------------\)
2. \(-2(2x^2+4x)=-(-3x^2-11x) \\ \Leftrightarrow -4x^2-8x=3x^2+11x \\ \Leftrightarrow -4x^2-8x-3x^2-11x= 0 \\ \Leftrightarrow -7x^2+19x=0 \\ \Leftrightarrow x(-7x+19) = 0 \\ \Leftrightarrow x = 0 \vee -7x+19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-19}{-7} = \frac{19}{7} \\ V = \Big\{ \frac{19}{7}; 0 \Big\} \\ -----------------\)
3. \(2(-8x^2+8x)=-(15x^2+2x) \\ \Leftrightarrow -16x^2+16x=-15x^2-2x \\ \Leftrightarrow -16x^2+16x+15x^2+2x= 0 \\ \Leftrightarrow -x^2-18x=0 \\ \Leftrightarrow x(-x-18) = 0 \\ \Leftrightarrow x = 0 \vee -x-18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{18}{-1} = -18 \\ V = \Big\{ 0 ; -18 \Big\} \\ -----------------\)
4. \(-3(-9x^2+5x)=-(-30x^2+31x) \\ \Leftrightarrow 27x^2-15x=30x^2-31x \\ \Leftrightarrow 27x^2-15x-30x^2+31x= 0 \\ \Leftrightarrow -3x^2-16x=0 \\ \Leftrightarrow x(-3x-16) = 0 \\ \Leftrightarrow x = 0 \vee -3x-16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{16}{-3} = \frac{-16}{3} \\ V = \Big\{ 0 ; \frac{-16}{3} \Big\} \\ -----------------\)
5. \(-7x^2-16x=0 \\ \Leftrightarrow x(-7x-16) = 0 \\ \Leftrightarrow x = 0 \vee -7x-16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{16}{-7} = \frac{-16}{7} \\ V = \Big\{ 0 ; \frac{-16}{7} \Big\} \\ -----------------\)
6. \(x^2-10x=0 \\ \Leftrightarrow x(x-10) = 0 \\ \Leftrightarrow x = 0 \vee x-10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{10}{1} = 10 \\ V = \Big\{ 10; 0 \Big\} \\ -----------------\)
7. \(4(7x^2-2x)=-(-26x^2-4x) \\ \Leftrightarrow 28x^2-8x=26x^2+4x \\ \Leftrightarrow 28x^2-8x-26x^2-4x= 0 \\ \Leftrightarrow 2x^2+12x=0 \\ \Leftrightarrow x(2x+12) = 0 \\ \Leftrightarrow x = 0 \vee 2x+12=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-12}{2} = -6 \\ V = \Big\{ 0 ; -6 \Big\} \\ -----------------\)
8. \(-8x^2+5x=0 \\ \Leftrightarrow x(-8x+5) = 0 \\ \Leftrightarrow x = 0 \vee -8x+5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-5}{-8} = \frac{5}{8} \\ V = \Big\{ \frac{5}{8}; 0 \Big\} \\ -----------------\)
9. \(-4(-2x^2+8x)=-(-16x^2+9x) \\ \Leftrightarrow 8x^2-32x=16x^2-9x \\ \Leftrightarrow 8x^2-32x-16x^2+9x= 0 \\ \Leftrightarrow -8x^2+23x=0 \\ \Leftrightarrow x(-8x+23) = 0 \\ \Leftrightarrow x = 0 \vee -8x+23=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-23}{-8} = \frac{23}{8} \\ V = \Big\{ \frac{23}{8}; 0 \Big\} \\ -----------------\)
10. \(-5x^2-21x=0 \\ \Leftrightarrow x(-5x-21) = 0 \\ \Leftrightarrow x = 0 \vee -5x-21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{21}{-5} = \frac{-21}{5} \\ V = \Big\{ 0 ; \frac{-21}{5} \Big\} \\ -----------------\)
11. \(-5x^2+7x=-2x^2-10x \\ \Leftrightarrow -3x^2+17x=0 \\ \Leftrightarrow x(-3x+17) = 0 \\ \Leftrightarrow x = 0 \vee -3x+17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-17}{-3} = \frac{17}{3} \\ V = \Big\{ \frac{17}{3}; 0 \Big\} \\ -----------------\)
12. \(-4x^2-15x=-3x^2+8x \\ \Leftrightarrow -x^2-23x=0 \\ \Leftrightarrow x(-x-23) = 0 \\ \Leftrightarrow x = 0 \vee -x-23=0 \\ \Leftrightarrow x = 0 \vee x = \frac{23}{-1} = -23 \\ V = \Big\{ 0 ; -23 \Big\} \\ -----------------\)