Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(9x^2-10x=8x^2-3x\)
2. \(-11x^2-16x=-6x^2+5x\)
3. \(-5(-6x^2+7x)=-(-26x^2+52x)\)
4. \(-8x^2+24x=-3x^2+3x\)
5. \(-13x^2+15x=-10x^2-3x\)
6. \(3(9x^2-6x)=-(-20x^2+23x)\)
7. \(3(2x^2+5x)=-(-5x^2-6x)\)
8. \(-5(5x^2-4x)=-(28x^2-12x)\)
9. \(6x^2-12x=0\)
10. \(6x^2+15x=2x^2+3x\)
11. \(8x^2-1x=0\)
12. \(14x^2-2x=8x^2+9x\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(9x^2-10x=8x^2-3x \\ \Leftrightarrow x^2-7x=0 \\ \Leftrightarrow x(x-7) = 0 \\ \Leftrightarrow x = 0 \vee x-7=0 \\ \Leftrightarrow x = 0 \vee x = \frac{7}{1} = 7 \\ V = \Big\{ 7; 0 \Big\} \\ -----------------\)
2. \(-11x^2-16x=-6x^2+5x \\ \Leftrightarrow -5x^2-21x=0 \\ \Leftrightarrow x(-5x-21) = 0 \\ \Leftrightarrow x = 0 \vee -5x-21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{21}{-5} = \frac{-21}{5} \\ V = \Big\{ 0 ; \frac{-21}{5} \Big\} \\ -----------------\)
3. \(-5(-6x^2+7x)=-(-26x^2+52x) \\ \Leftrightarrow 30x^2-35x=26x^2-52x \\ \Leftrightarrow 30x^2-35x-26x^2+52x= 0 \\ \Leftrightarrow 4x^2-17x=0 \\ \Leftrightarrow x(4x-17) = 0 \\ \Leftrightarrow x = 0 \vee 4x-17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{17}{4} \\ V = \Big\{ \frac{17}{4}; 0 \Big\} \\ -----------------\)
4. \(-8x^2+24x=-3x^2+3x \\ \Leftrightarrow -5x^2+21x=0 \\ \Leftrightarrow x(-5x+21) = 0 \\ \Leftrightarrow x = 0 \vee -5x+21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-21}{-5} = \frac{21}{5} \\ V = \Big\{ \frac{21}{5}; 0 \Big\} \\ -----------------\)
5. \(-13x^2+15x=-10x^2-3x \\ \Leftrightarrow -3x^2+18x=0 \\ \Leftrightarrow x(-3x+18) = 0 \\ \Leftrightarrow x = 0 \vee -3x+18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-18}{-3} = 6 \\ V = \Big\{ 6; 0 \Big\} \\ -----------------\)
6. \(3(9x^2-6x)=-(-20x^2+23x) \\ \Leftrightarrow 27x^2-18x=20x^2-23x \\ \Leftrightarrow 27x^2-18x-20x^2+23x= 0 \\ \Leftrightarrow 7x^2-5x=0 \\ \Leftrightarrow x(7x-5) = 0 \\ \Leftrightarrow x = 0 \vee 7x-5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{5}{7} \\ V = \Big\{ \frac{5}{7}; 0 \Big\} \\ -----------------\)
7. \(3(2x^2+5x)=-(-5x^2-6x) \\ \Leftrightarrow 6x^2+15x=5x^2+6x \\ \Leftrightarrow 6x^2+15x-5x^2-6x= 0 \\ \Leftrightarrow x^2-9x=0 \\ \Leftrightarrow x(x-9) = 0 \\ \Leftrightarrow x = 0 \vee x-9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{9}{1} = 9 \\ V = \Big\{ 9; 0 \Big\} \\ -----------------\)
8. \(-5(5x^2-4x)=-(28x^2-12x) \\ \Leftrightarrow -25x^2+20x=-28x^2+12x \\ \Leftrightarrow -25x^2+20x+28x^2-12x= 0 \\ \Leftrightarrow 3x^2-8x=0 \\ \Leftrightarrow x(3x-8) = 0 \\ \Leftrightarrow x = 0 \vee 3x-8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{8}{3} \\ V = \Big\{ \frac{8}{3}; 0 \Big\} \\ -----------------\)
9. \(6x^2-12x=0 \\ \Leftrightarrow x(6x-12) = 0 \\ \Leftrightarrow x = 0 \vee 6x-12=0 \\ \Leftrightarrow x = 0 \vee x = \frac{12}{6} = 2 \\ V = \Big\{ 2; 0 \Big\} \\ -----------------\)
10. \(6x^2+15x=2x^2+3x \\ \Leftrightarrow 4x^2+12x=0 \\ \Leftrightarrow x(4x+12) = 0 \\ \Leftrightarrow x = 0 \vee 4x+12=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-12}{4} = -3 \\ V = \Big\{ 0 ; -3 \Big\} \\ -----------------\)
11. \(8x^2-1x=0 \\ \Leftrightarrow x(8x-1) = 0 \\ \Leftrightarrow x = 0 \vee 8x-1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{1}{8} \\ V = \Big\{ \frac{1}{8}; 0 \Big\} \\ -----------------\)
12. \(14x^2-2x=8x^2+9x \\ \Leftrightarrow 6x^2-11x=0 \\ \Leftrightarrow x(6x-11) = 0 \\ \Leftrightarrow x = 0 \vee 6x-11=0 \\ \Leftrightarrow x = 0 \vee x = \frac{11}{6} \\ V = \Big\{ \frac{11}{6}; 0 \Big\} \\ -----------------\)