Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-4(2x^2-8x)=-(7x^2-33x)\)
2. \(5x^2+20x=4x^2+8x\)
3. \(-3x^2+5x=-2x^2-2x\)
4. \(-2x^2-9x=0\)
5. \(-8x^2-9x=0\)
6. \(-2x^2-22x=0\)
7. \(3(-2x^2-3x)=-(13x^2-12x)\)
8. \(8x^2-3x=0\)
9. \(-4(-8x^2-9x)=-(-37x^2-52x)\)
10. \(-4x^2+25x=0\)
11. \(-5(-5x^2+8x)=-(-21x^2+42x)\)
12. \(5(2x^2-2x)=-(-6x^2+9x)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-4(2x^2-8x)=-(7x^2-33x) \\ \Leftrightarrow -8x^2+32x=-7x^2+33x \\ \Leftrightarrow -8x^2+32x+7x^2-33x= 0 \\ \Leftrightarrow -x^2+1x=0 \\ \Leftrightarrow x(-x+1) = 0 \\ \Leftrightarrow x = 0 \vee -x+1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-1}{-1} = 1 \\ V = \Big\{ 1; 0 \Big\} \\ -----------------\)
2. \(5x^2+20x=4x^2+8x \\ \Leftrightarrow x^2+12x=0 \\ \Leftrightarrow x(x+12) = 0 \\ \Leftrightarrow x = 0 \vee x+12=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-12}{1} = -12 \\ V = \Big\{ 0 ; -12 \Big\} \\ -----------------\)
3. \(-3x^2+5x=-2x^2-2x \\ \Leftrightarrow -x^2+7x=0 \\ \Leftrightarrow x(-x+7) = 0 \\ \Leftrightarrow x = 0 \vee -x+7=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-7}{-1} = 7 \\ V = \Big\{ 7; 0 \Big\} \\ -----------------\)
4. \(-2x^2-9x=0 \\ \Leftrightarrow x(-2x-9) = 0 \\ \Leftrightarrow x = 0 \vee -2x-9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{9}{-2} = \frac{-9}{2} \\ V = \Big\{ 0 ; \frac{-9}{2} \Big\} \\ -----------------\)
5. \(-8x^2-9x=0 \\ \Leftrightarrow x(-8x-9) = 0 \\ \Leftrightarrow x = 0 \vee -8x-9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{9}{-8} = \frac{-9}{8} \\ V = \Big\{ 0 ; \frac{-9}{8} \Big\} \\ -----------------\)
6. \(-2x^2-22x=0 \\ \Leftrightarrow x(-2x-22) = 0 \\ \Leftrightarrow x = 0 \vee -2x-22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{22}{-2} = -11 \\ V = \Big\{ 0 ; -11 \Big\} \\ -----------------\)
7. \(3(-2x^2-3x)=-(13x^2-12x) \\ \Leftrightarrow -6x^2-9x=-13x^2+12x \\ \Leftrightarrow -6x^2-9x+13x^2-12x= 0 \\ \Leftrightarrow 7x^2+21x=0 \\ \Leftrightarrow x(7x+21) = 0 \\ \Leftrightarrow x = 0 \vee 7x+21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-21}{7} = -3 \\ V = \Big\{ 0 ; -3 \Big\} \\ -----------------\)
8. \(8x^2-3x=0 \\ \Leftrightarrow x(8x-3) = 0 \\ \Leftrightarrow x = 0 \vee 8x-3=0 \\ \Leftrightarrow x = 0 \vee x = \frac{3}{8} \\ V = \Big\{ \frac{3}{8}; 0 \Big\} \\ -----------------\)
9. \(-4(-8x^2-9x)=-(-37x^2-52x) \\ \Leftrightarrow 32x^2+36x=37x^2+52x \\ \Leftrightarrow 32x^2+36x-37x^2-52x= 0 \\ \Leftrightarrow -5x^2+16x=0 \\ \Leftrightarrow x(-5x+16) = 0 \\ \Leftrightarrow x = 0 \vee -5x+16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-16}{-5} = \frac{16}{5} \\ V = \Big\{ \frac{16}{5}; 0 \Big\} \\ -----------------\)
10. \(-4x^2+25x=0 \\ \Leftrightarrow x(-4x+25) = 0 \\ \Leftrightarrow x = 0 \vee -4x+25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-25}{-4} = \frac{25}{4} \\ V = \Big\{ \frac{25}{4}; 0 \Big\} \\ -----------------\)
11. \(-5(-5x^2+8x)=-(-21x^2+42x) \\ \Leftrightarrow 25x^2-40x=21x^2-42x \\ \Leftrightarrow 25x^2-40x-21x^2+42x= 0 \\ \Leftrightarrow 4x^2-2x=0 \\ \Leftrightarrow x(4x-2) = 0 \\ \Leftrightarrow x = 0 \vee 4x-2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{2}{4} = \frac{1}{2} \\ V = \Big\{ \frac{1}{2}; 0 \Big\} \\ -----------------\)
12. \(5(2x^2-2x)=-(-6x^2+9x) \\ \Leftrightarrow 10x^2-10x=6x^2-9x \\ \Leftrightarrow 10x^2-10x-6x^2+9x= 0 \\ \Leftrightarrow 4x^2+1x=0 \\ \Leftrightarrow x(4x+1) = 0 \\ \Leftrightarrow x = 0 \vee 4x+1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-1}{4} \\ V = \Big\{ 0 ; \frac{-1}{4} \Big\} \\ -----------------\)