Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(4(9x^2+7x)=-(-30x^2-13x)\)
2. \(-5(6x^2-7x)=-(34x^2-16x)\)
3. \(8x^2+0x=0\)
4. \(2(-2x^2-9x)=-(0x^2+8x)\)
5. \(-5x^2-7x=-8x^2+4x\)
6. \(-3(-8x^2-9x)=-(-27x^2-2x)\)
7. \(-4(2x^2-2x)=-(16x^2-18x)\)
8. \(x^2-11x=6x^2+5x\)
9. \(5(-5x^2-10x)=-(27x^2+48x)\)
10. \(-5x^2+5x=0\)
11. \(-x^2-6x=0\)
12. \(-4(5x^2+5x)=-(16x^2+37x)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(4(9x^2+7x)=-(-30x^2-13x) \\ \Leftrightarrow 36x^2+28x=30x^2+13x \\ \Leftrightarrow 36x^2+28x-30x^2-13x= 0 \\ \Leftrightarrow 6x^2-15x=0 \\ \Leftrightarrow x(6x-15) = 0 \\ \Leftrightarrow x = 0 \vee 6x-15=0 \\ \Leftrightarrow x = 0 \vee x = \frac{15}{6} = \frac{5}{2} \\ V = \Big\{ \frac{5}{2}; 0 \Big\} \\ -----------------\)
2. \(-5(6x^2-7x)=-(34x^2-16x) \\ \Leftrightarrow -30x^2+35x=-34x^2+16x \\ \Leftrightarrow -30x^2+35x+34x^2-16x= 0 \\ \Leftrightarrow 4x^2-19x=0 \\ \Leftrightarrow x(4x-19) = 0 \\ \Leftrightarrow x = 0 \vee 4x-19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{19}{4} \\ V = \Big\{ \frac{19}{4}; 0 \Big\} \\ -----------------\)
3. \(8x^2+0x=0 \\ \Leftrightarrow 8x^2=0 \\ \Leftrightarrow x^2 = \frac{0}{8} \\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
4. \(2(-2x^2-9x)=-(0x^2+8x) \\ \Leftrightarrow -4x^2-18x=0x^2-8x \\ \Leftrightarrow -4x^2-18x+0x^2+8x= 0 \\ \Leftrightarrow -4x^2+10x=0 \\ \Leftrightarrow x(-4x+10) = 0 \\ \Leftrightarrow x = 0 \vee -4x+10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-10}{-4} = \frac{5}{2} \\ V = \Big\{ \frac{5}{2}; 0 \Big\} \\ -----------------\)
5. \(-5x^2-7x=-8x^2+4x \\ \Leftrightarrow 3x^2-11x=0 \\ \Leftrightarrow x(3x-11) = 0 \\ \Leftrightarrow x = 0 \vee 3x-11=0 \\ \Leftrightarrow x = 0 \vee x = \frac{11}{3} \\ V = \Big\{ \frac{11}{3}; 0 \Big\} \\ -----------------\)
6. \(-3(-8x^2-9x)=-(-27x^2-2x) \\ \Leftrightarrow 24x^2+27x=27x^2+2x \\ \Leftrightarrow 24x^2+27x-27x^2-2x= 0 \\ \Leftrightarrow -3x^2-25x=0 \\ \Leftrightarrow x(-3x-25) = 0 \\ \Leftrightarrow x = 0 \vee -3x-25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{25}{-3} = \frac{-25}{3} \\ V = \Big\{ 0 ; \frac{-25}{3} \Big\} \\ -----------------\)
7. \(-4(2x^2-2x)=-(16x^2-18x) \\ \Leftrightarrow -8x^2+8x=-16x^2+18x \\ \Leftrightarrow -8x^2+8x+16x^2-18x= 0 \\ \Leftrightarrow 8x^2+10x=0 \\ \Leftrightarrow x(8x+10) = 0 \\ \Leftrightarrow x = 0 \vee 8x+10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-10}{8} = \frac{-5}{4} \\ V = \Big\{ 0 ; \frac{-5}{4} \Big\} \\ -----------------\)
8. \(x^2-11x=6x^2+5x \\ \Leftrightarrow -5x^2-16x=0 \\ \Leftrightarrow x(-5x-16) = 0 \\ \Leftrightarrow x = 0 \vee -5x-16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{16}{-5} = \frac{-16}{5} \\ V = \Big\{ 0 ; \frac{-16}{5} \Big\} \\ -----------------\)
9. \(5(-5x^2-10x)=-(27x^2+48x) \\ \Leftrightarrow -25x^2-50x=-27x^2-48x \\ \Leftrightarrow -25x^2-50x+27x^2+48x= 0 \\ \Leftrightarrow 2x^2+2x=0 \\ \Leftrightarrow x(2x+2) = 0 \\ \Leftrightarrow x = 0 \vee 2x+2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-2}{2} = -1 \\ V = \Big\{ 0 ; -1 \Big\} \\ -----------------\)
10. \(-5x^2+5x=0 \\ \Leftrightarrow x(-5x+5) = 0 \\ \Leftrightarrow x = 0 \vee -5x+5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-5}{-5} = 1 \\ V = \Big\{ 1; 0 \Big\} \\ -----------------\)
11. \(-x^2-6x=0 \\ \Leftrightarrow x(-x-6) = 0 \\ \Leftrightarrow x = 0 \vee -x-6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{6}{-1} = -6 \\ V = \Big\{ 0 ; -6 \Big\} \\ -----------------\)
12. \(-4(5x^2+5x)=-(16x^2+37x) \\ \Leftrightarrow -20x^2-20x=-16x^2-37x \\ \Leftrightarrow -20x^2-20x+16x^2+37x= 0 \\ \Leftrightarrow -4x^2-17x=0 \\ \Leftrightarrow x(-4x-17) = 0 \\ \Leftrightarrow x = 0 \vee -4x-17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{17}{-4} = \frac{-17}{4} \\ V = \Big\{ 0 ; \frac{-17}{4} \Big\} \\ -----------------\)