Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-4(5x^2-8x)=-(21x^2-13x)\)
2. \(-5x^2-2x=-7x^2+9x\)
3. \(2(-2x^2-10x)=-(8x^2+37x)\)
4. \(4x^2+21x=9x^2-3x\)
5. \(3(5x^2+2x)=-(-7x^2-5x)\)
6. \(4(6x^2+9x)=-(-28x^2-21x)\)
7. \(-3(-10x^2+9x)=-(-32x^2+44x)\)
8. \(2(4x^2-7x)=-(-3x^2-6x)\)
9. \(-2(-3x^2+10x)=-(-13x^2+40x)\)
10. \(-2(6x^2-4x)=-(17x^2+17x)\)
11. \(8x^2-19x=0\)
12. \(4(-5x^2-7x)=-(13x^2+37x)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-4(5x^2-8x)=-(21x^2-13x) \\ \Leftrightarrow -20x^2+32x=-21x^2+13x \\ \Leftrightarrow -20x^2+32x+21x^2-13x= 0 \\ \Leftrightarrow x^2-19x=0 \\ \Leftrightarrow x(x-19) = 0 \\ \Leftrightarrow x = 0 \vee x-19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{19}{1} = 19 \\ V = \Big\{ 19; 0 \Big\} \\ -----------------\)
2. \(-5x^2-2x=-7x^2+9x \\ \Leftrightarrow 2x^2-11x=0 \\ \Leftrightarrow x(2x-11) = 0 \\ \Leftrightarrow x = 0 \vee 2x-11=0 \\ \Leftrightarrow x = 0 \vee x = \frac{11}{2} \\ V = \Big\{ \frac{11}{2}; 0 \Big\} \\ -----------------\)
3. \(2(-2x^2-10x)=-(8x^2+37x) \\ \Leftrightarrow -4x^2-20x=-8x^2-37x \\ \Leftrightarrow -4x^2-20x+8x^2+37x= 0 \\ \Leftrightarrow 4x^2-17x=0 \\ \Leftrightarrow x(4x-17) = 0 \\ \Leftrightarrow x = 0 \vee 4x-17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{17}{4} \\ V = \Big\{ \frac{17}{4}; 0 \Big\} \\ -----------------\)
4. \(4x^2+21x=9x^2-3x \\ \Leftrightarrow -5x^2+24x=0 \\ \Leftrightarrow x(-5x+24) = 0 \\ \Leftrightarrow x = 0 \vee -5x+24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-24}{-5} = \frac{24}{5} \\ V = \Big\{ \frac{24}{5}; 0 \Big\} \\ -----------------\)
5. \(3(5x^2+2x)=-(-7x^2-5x) \\ \Leftrightarrow 15x^2+6x=7x^2+5x \\ \Leftrightarrow 15x^2+6x-7x^2-5x= 0 \\ \Leftrightarrow 8x^2-1x=0 \\ \Leftrightarrow x(8x-1) = 0 \\ \Leftrightarrow x = 0 \vee 8x-1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{1}{8} \\ V = \Big\{ \frac{1}{8}; 0 \Big\} \\ -----------------\)
6. \(4(6x^2+9x)=-(-28x^2-21x) \\ \Leftrightarrow 24x^2+36x=28x^2+21x \\ \Leftrightarrow 24x^2+36x-28x^2-21x= 0 \\ \Leftrightarrow -4x^2-15x=0 \\ \Leftrightarrow x(-4x-15) = 0 \\ \Leftrightarrow x = 0 \vee -4x-15=0 \\ \Leftrightarrow x = 0 \vee x = \frac{15}{-4} = \frac{-15}{4} \\ V = \Big\{ 0 ; \frac{-15}{4} \Big\} \\ -----------------\)
7. \(-3(-10x^2+9x)=-(-32x^2+44x) \\ \Leftrightarrow 30x^2-27x=32x^2-44x \\ \Leftrightarrow 30x^2-27x-32x^2+44x= 0 \\ \Leftrightarrow -2x^2-17x=0 \\ \Leftrightarrow x(-2x-17) = 0 \\ \Leftrightarrow x = 0 \vee -2x-17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{17}{-2} = \frac{-17}{2} \\ V = \Big\{ 0 ; \frac{-17}{2} \Big\} \\ -----------------\)
8. \(2(4x^2-7x)=-(-3x^2-6x) \\ \Leftrightarrow 8x^2-14x=3x^2+6x \\ \Leftrightarrow 8x^2-14x-3x^2-6x= 0 \\ \Leftrightarrow 5x^2+20x=0 \\ \Leftrightarrow x(5x+20) = 0 \\ \Leftrightarrow x = 0 \vee 5x+20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-20}{5} = -4 \\ V = \Big\{ 0 ; -4 \Big\} \\ -----------------\)
9. \(-2(-3x^2+10x)=-(-13x^2+40x) \\ \Leftrightarrow 6x^2-20x=13x^2-40x \\ \Leftrightarrow 6x^2-20x-13x^2+40x= 0 \\ \Leftrightarrow -7x^2-20x=0 \\ \Leftrightarrow x(-7x-20) = 0 \\ \Leftrightarrow x = 0 \vee -7x-20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{20}{-7} = \frac{-20}{7} \\ V = \Big\{ 0 ; \frac{-20}{7} \Big\} \\ -----------------\)
10. \(-2(6x^2-4x)=-(17x^2+17x) \\ \Leftrightarrow -12x^2+8x=-17x^2-17x \\ \Leftrightarrow -12x^2+8x+17x^2+17x= 0 \\ \Leftrightarrow 5x^2-25x=0 \\ \Leftrightarrow x(5x-25) = 0 \\ \Leftrightarrow x = 0 \vee 5x-25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{25}{5} = 5 \\ V = \Big\{ 5; 0 \Big\} \\ -----------------\)
11. \(8x^2-19x=0 \\ \Leftrightarrow x(8x-19) = 0 \\ \Leftrightarrow x = 0 \vee 8x-19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{19}{8} \\ V = \Big\{ \frac{19}{8}; 0 \Big\} \\ -----------------\)
12. \(4(-5x^2-7x)=-(13x^2+37x) \\ \Leftrightarrow -20x^2-28x=-13x^2-37x \\ \Leftrightarrow -20x^2-28x+13x^2+37x= 0 \\ \Leftrightarrow -7x^2-9x=0 \\ \Leftrightarrow x(-7x-9) = 0 \\ \Leftrightarrow x = 0 \vee -7x-9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{9}{-7} = \frac{-9}{7} \\ V = \Big\{ 0 ; \frac{-9}{7} \Big\} \\ -----------------\)