Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(3(-7x^2-5x)=-(22x^2+13x)\)
2. \(-7x^2+25x=0\)
3. \(12x^2-7x=9x^2-3x\)
4. \(6x^2-11x=5x^2-2x\)
5. \(4x^2-15x=0\)
6. \(-3(-5x^2-9x)=-(-7x^2-4x)\)
7. \(4x^2+21x=0\)
8. \(-2(3x^2-2x)=-(7x^2+x)\)
9. \(-x^2-24x=0\)
10. \(-4x^2-8x=0\)
11. \(-4x^2-14x=4x^2+4x\)
12. \(-4x^2+9x=-7x^2-8x\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(3(-7x^2-5x)=-(22x^2+13x) \\ \Leftrightarrow -21x^2-15x=-22x^2-13x \\ \Leftrightarrow -21x^2-15x+22x^2+13x= 0 \\ \Leftrightarrow x^2+2x=0 \\ \Leftrightarrow x(x+2) = 0 \\ \Leftrightarrow x = 0 \vee x+2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-2}{1} = -2 \\ V = \Big\{ 0 ; -2 \Big\} \\ -----------------\)
2. \(-7x^2+25x=0 \\ \Leftrightarrow x(-7x+25) = 0 \\ \Leftrightarrow x = 0 \vee -7x+25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-25}{-7} = \frac{25}{7} \\ V = \Big\{ \frac{25}{7}; 0 \Big\} \\ -----------------\)
3. \(12x^2-7x=9x^2-3x \\ \Leftrightarrow 3x^2-4x=0 \\ \Leftrightarrow x(3x-4) = 0 \\ \Leftrightarrow x = 0 \vee 3x-4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{4}{3} \\ V = \Big\{ \frac{4}{3}; 0 \Big\} \\ -----------------\)
4. \(6x^2-11x=5x^2-2x \\ \Leftrightarrow x^2-9x=0 \\ \Leftrightarrow x(x-9) = 0 \\ \Leftrightarrow x = 0 \vee x-9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{9}{1} = 9 \\ V = \Big\{ 9; 0 \Big\} \\ -----------------\)
5. \(4x^2-15x=0 \\ \Leftrightarrow x(4x-15) = 0 \\ \Leftrightarrow x = 0 \vee 4x-15=0 \\ \Leftrightarrow x = 0 \vee x = \frac{15}{4} \\ V = \Big\{ \frac{15}{4}; 0 \Big\} \\ -----------------\)
6. \(-3(-5x^2-9x)=-(-7x^2-4x) \\ \Leftrightarrow 15x^2+27x=7x^2+4x \\ \Leftrightarrow 15x^2+27x-7x^2-4x= 0 \\ \Leftrightarrow 8x^2-23x=0 \\ \Leftrightarrow x(8x-23) = 0 \\ \Leftrightarrow x = 0 \vee 8x-23=0 \\ \Leftrightarrow x = 0 \vee x = \frac{23}{8} \\ V = \Big\{ \frac{23}{8}; 0 \Big\} \\ -----------------\)
7. \(4x^2+21x=0 \\ \Leftrightarrow x(4x+21) = 0 \\ \Leftrightarrow x = 0 \vee 4x+21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-21}{4} \\ V = \Big\{ 0 ; \frac{-21}{4} \Big\} \\ -----------------\)
8. \(-2(3x^2-2x)=-(7x^2+x) \\ \Leftrightarrow -6x^2+4x=-7x^2-x \\ \Leftrightarrow -6x^2+4x+7x^2+x= 0 \\ \Leftrightarrow x^2-5x=0 \\ \Leftrightarrow x(x-5) = 0 \\ \Leftrightarrow x = 0 \vee x-5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{5}{1} = 5 \\ V = \Big\{ 5; 0 \Big\} \\ -----------------\)
9. \(-x^2-24x=0 \\ \Leftrightarrow x(-x-24) = 0 \\ \Leftrightarrow x = 0 \vee -x-24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{24}{-1} = -24 \\ V = \Big\{ 0 ; -24 \Big\} \\ -----------------\)
10. \(-4x^2-8x=0 \\ \Leftrightarrow x(-4x-8) = 0 \\ \Leftrightarrow x = 0 \vee -4x-8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{8}{-4} = -2 \\ V = \Big\{ 0 ; -2 \Big\} \\ -----------------\)
11. \(-4x^2-14x=4x^2+4x \\ \Leftrightarrow -8x^2-18x=0 \\ \Leftrightarrow x(-8x-18) = 0 \\ \Leftrightarrow x = 0 \vee -8x-18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{18}{-8} = \frac{-9}{4} \\ V = \Big\{ 0 ; \frac{-9}{4} \Big\} \\ -----------------\)
12. \(-4x^2+9x=-7x^2-8x \\ \Leftrightarrow 3x^2+17x=0 \\ \Leftrightarrow x(3x+17) = 0 \\ \Leftrightarrow x = 0 \vee 3x+17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-17}{3} \\ V = \Big\{ 0 ; \frac{-17}{3} \Big\} \\ -----------------\)