Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(10x^2+15x=7x^2+5x\)
2. \(4(-4x^2-5x)=-(18x^2+11x)\)
3. \(3(-9x^2-7x)=-(34x^2+18x)\)
4. \(5(-7x^2-8x)=-(27x^2+31x)\)
5. \(2x^2-27x=-2x^2-6x\)
6. \(-5x^2-1x=0\)
7. \(-x^2-20x=4x^2-5x\)
8. \(4(4x^2-5x)=-(-17x^2+11x)\)
9. \(4(8x^2+5x)=-(-25x^2-4x)\)
10. \(-4(7x^2-5x)=-(26x^2-43x)\)
11. \(-5(-6x^2+9x)=-(-37x^2+60x)\)
12. \(9x^2-13x=7x^2+7x\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(10x^2+15x=7x^2+5x \\ \Leftrightarrow 3x^2+10x=0 \\ \Leftrightarrow x(3x+10) = 0 \\ \Leftrightarrow x = 0 \vee 3x+10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-10}{3} \\ V = \Big\{ 0 ; \frac{-10}{3} \Big\} \\ -----------------\)
2. \(4(-4x^2-5x)=-(18x^2+11x) \\ \Leftrightarrow -16x^2-20x=-18x^2-11x \\ \Leftrightarrow -16x^2-20x+18x^2+11x= 0 \\ \Leftrightarrow 2x^2+9x=0 \\ \Leftrightarrow x(2x+9) = 0 \\ \Leftrightarrow x = 0 \vee 2x+9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-9}{2} \\ V = \Big\{ 0 ; \frac{-9}{2} \Big\} \\ -----------------\)
3. \(3(-9x^2-7x)=-(34x^2+18x) \\ \Leftrightarrow -27x^2-21x=-34x^2-18x \\ \Leftrightarrow -27x^2-21x+34x^2+18x= 0 \\ \Leftrightarrow 7x^2+3x=0 \\ \Leftrightarrow x(7x+3) = 0 \\ \Leftrightarrow x = 0 \vee 7x+3=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-3}{7} \\ V = \Big\{ 0 ; \frac{-3}{7} \Big\} \\ -----------------\)
4. \(5(-7x^2-8x)=-(27x^2+31x) \\ \Leftrightarrow -35x^2-40x=-27x^2-31x \\ \Leftrightarrow -35x^2-40x+27x^2+31x= 0 \\ \Leftrightarrow -8x^2+9x=0 \\ \Leftrightarrow x(-8x+9) = 0 \\ \Leftrightarrow x = 0 \vee -8x+9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-9}{-8} = \frac{9}{8} \\ V = \Big\{ \frac{9}{8}; 0 \Big\} \\ -----------------\)
5. \(2x^2-27x=-2x^2-6x \\ \Leftrightarrow 4x^2-21x=0 \\ \Leftrightarrow x(4x-21) = 0 \\ \Leftrightarrow x = 0 \vee 4x-21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{21}{4} \\ V = \Big\{ \frac{21}{4}; 0 \Big\} \\ -----------------\)
6. \(-5x^2-1x=0 \\ \Leftrightarrow x(-5x-1) = 0 \\ \Leftrightarrow x = 0 \vee -5x-1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{1}{-5} = \frac{-1}{5} \\ V = \Big\{ 0 ; \frac{-1}{5} \Big\} \\ -----------------\)
7. \(-x^2-20x=4x^2-5x \\ \Leftrightarrow -5x^2-15x=0 \\ \Leftrightarrow x(-5x-15) = 0 \\ \Leftrightarrow x = 0 \vee -5x-15=0 \\ \Leftrightarrow x = 0 \vee x = \frac{15}{-5} = -3 \\ V = \Big\{ 0 ; -3 \Big\} \\ -----------------\)
8. \(4(4x^2-5x)=-(-17x^2+11x) \\ \Leftrightarrow 16x^2-20x=17x^2-11x \\ \Leftrightarrow 16x^2-20x-17x^2+11x= 0 \\ \Leftrightarrow -x^2+9x=0 \\ \Leftrightarrow x(-x+9) = 0 \\ \Leftrightarrow x = 0 \vee -x+9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-9}{-1} = 9 \\ V = \Big\{ 9; 0 \Big\} \\ -----------------\)
9. \(4(8x^2+5x)=-(-25x^2-4x) \\ \Leftrightarrow 32x^2+20x=25x^2+4x \\ \Leftrightarrow 32x^2+20x-25x^2-4x= 0 \\ \Leftrightarrow 7x^2-16x=0 \\ \Leftrightarrow x(7x-16) = 0 \\ \Leftrightarrow x = 0 \vee 7x-16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{16}{7} \\ V = \Big\{ \frac{16}{7}; 0 \Big\} \\ -----------------\)
10. \(-4(7x^2-5x)=-(26x^2-43x) \\ \Leftrightarrow -28x^2+20x=-26x^2+43x \\ \Leftrightarrow -28x^2+20x+26x^2-43x= 0 \\ \Leftrightarrow -2x^2+23x=0 \\ \Leftrightarrow x(-2x+23) = 0 \\ \Leftrightarrow x = 0 \vee -2x+23=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-23}{-2} = \frac{23}{2} \\ V = \Big\{ \frac{23}{2}; 0 \Big\} \\ -----------------\)
11. \(-5(-6x^2+9x)=-(-37x^2+60x) \\ \Leftrightarrow 30x^2-45x=37x^2-60x \\ \Leftrightarrow 30x^2-45x-37x^2+60x= 0 \\ \Leftrightarrow -7x^2-15x=0 \\ \Leftrightarrow x(-7x-15) = 0 \\ \Leftrightarrow x = 0 \vee -7x-15=0 \\ \Leftrightarrow x = 0 \vee x = \frac{15}{-7} = \frac{-15}{7} \\ V = \Big\{ 0 ; \frac{-15}{7} \Big\} \\ -----------------\)
12. \(9x^2-13x=7x^2+7x \\ \Leftrightarrow 2x^2-20x=0 \\ \Leftrightarrow x(2x-20) = 0 \\ \Leftrightarrow x = 0 \vee 2x-20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{20}{2} = 10 \\ V = \Big\{ 10; 0 \Big\} \\ -----------------\)