Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(10x^2+11x=9x^2-10x\)
2. \(3x^2+17x=10x^2-8x\)
3. \(2(-4x^2-2x)=-(10x^2+5x)\)
4. \(-2(3x^2-7x)=-(12x^2-26x)\)
5. \(8x^2-25x=0\)
6. \(2(5x^2-6x)=-(-7x^2+36x)\)
7. \(8x^2-12x=2x^2+2x\)
8. \(5(-10x^2+3x)=-(44x^2+6x)\)
9. \(7x^2+1x=0\)
10. \(-x^2-18x=-3x^2-10x\)
11. \(2x^2-12x=-6x^2+10x\)
12. \(-6x^2-8x=-8x^2+7x\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(10x^2+11x=9x^2-10x \\ \Leftrightarrow x^2+21x=0 \\ \Leftrightarrow x(x+21) = 0 \\ \Leftrightarrow x = 0 \vee x+21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-21}{1} = -21 \\ V = \Big\{ 0 ; -21 \Big\} \\ -----------------\)
2. \(3x^2+17x=10x^2-8x \\ \Leftrightarrow -7x^2+25x=0 \\ \Leftrightarrow x(-7x+25) = 0 \\ \Leftrightarrow x = 0 \vee -7x+25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-25}{-7} = \frac{25}{7} \\ V = \Big\{ \frac{25}{7}; 0 \Big\} \\ -----------------\)
3. \(2(-4x^2-2x)=-(10x^2+5x) \\ \Leftrightarrow -8x^2-4x=-10x^2-5x \\ \Leftrightarrow -8x^2-4x+10x^2+5x= 0 \\ \Leftrightarrow 2x^2-1x=0 \\ \Leftrightarrow x(2x-1) = 0 \\ \Leftrightarrow x = 0 \vee 2x-1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{1}{2} \\ V = \Big\{ \frac{1}{2}; 0 \Big\} \\ -----------------\)
4. \(-2(3x^2-7x)=-(12x^2-26x) \\ \Leftrightarrow -6x^2+14x=-12x^2+26x \\ \Leftrightarrow -6x^2+14x+12x^2-26x= 0 \\ \Leftrightarrow 6x^2+12x=0 \\ \Leftrightarrow x(6x+12) = 0 \\ \Leftrightarrow x = 0 \vee 6x+12=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-12}{6} = -2 \\ V = \Big\{ 0 ; -2 \Big\} \\ -----------------\)
5. \(8x^2-25x=0 \\ \Leftrightarrow x(8x-25) = 0 \\ \Leftrightarrow x = 0 \vee 8x-25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{25}{8} \\ V = \Big\{ \frac{25}{8}; 0 \Big\} \\ -----------------\)
6. \(2(5x^2-6x)=-(-7x^2+36x) \\ \Leftrightarrow 10x^2-12x=7x^2-36x \\ \Leftrightarrow 10x^2-12x-7x^2+36x= 0 \\ \Leftrightarrow 3x^2-24x=0 \\ \Leftrightarrow x(3x-24) = 0 \\ \Leftrightarrow x = 0 \vee 3x-24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{24}{3} = 8 \\ V = \Big\{ 8; 0 \Big\} \\ -----------------\)
7. \(8x^2-12x=2x^2+2x \\ \Leftrightarrow 6x^2-14x=0 \\ \Leftrightarrow x(6x-14) = 0 \\ \Leftrightarrow x = 0 \vee 6x-14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{14}{6} = \frac{7}{3} \\ V = \Big\{ \frac{7}{3}; 0 \Big\} \\ -----------------\)
8. \(5(-10x^2+3x)=-(44x^2+6x) \\ \Leftrightarrow -50x^2+15x=-44x^2-6x \\ \Leftrightarrow -50x^2+15x+44x^2+6x= 0 \\ \Leftrightarrow -6x^2-21x=0 \\ \Leftrightarrow x(-6x-21) = 0 \\ \Leftrightarrow x = 0 \vee -6x-21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{21}{-6} = \frac{-7}{2} \\ V = \Big\{ 0 ; \frac{-7}{2} \Big\} \\ -----------------\)
9. \(7x^2+1x=0 \\ \Leftrightarrow x(7x+1) = 0 \\ \Leftrightarrow x = 0 \vee 7x+1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-1}{7} \\ V = \Big\{ 0 ; \frac{-1}{7} \Big\} \\ -----------------\)
10. \(-x^2-18x=-3x^2-10x \\ \Leftrightarrow 2x^2-8x=0 \\ \Leftrightarrow x(2x-8) = 0 \\ \Leftrightarrow x = 0 \vee 2x-8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{8}{2} = 4 \\ V = \Big\{ 4; 0 \Big\} \\ -----------------\)
11. \(2x^2-12x=-6x^2+10x \\ \Leftrightarrow 8x^2-22x=0 \\ \Leftrightarrow x(8x-22) = 0 \\ \Leftrightarrow x = 0 \vee 8x-22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{22}{8} = \frac{11}{4} \\ V = \Big\{ \frac{11}{4}; 0 \Big\} \\ -----------------\)
12. \(-6x^2-8x=-8x^2+7x \\ \Leftrightarrow 2x^2-15x=0 \\ \Leftrightarrow x(2x-15) = 0 \\ \Leftrightarrow x = 0 \vee 2x-15=0 \\ \Leftrightarrow x = 0 \vee x = \frac{15}{2} \\ V = \Big\{ \frac{15}{2}; 0 \Big\} \\ -----------------\)