Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(8x^2-12x=7x^2-2x\)
2. \(5x^2+5x=6x^2-10x\)
3. \(9x^2+3x=6x^2+5x\)
4. \(-8x^2-12x=-3x^2+10x\)
5. \(4x^2+8x=0\)
6. \(-7x^2+15x=0\)
7. \(x^2+15x=5x^2+6x\)
8. \(2(-5x^2+2x)=-(3x^2-14x)\)
9. \(-5(-6x^2-6x)=-(-35x^2-9x)\)
10. \(-5(-9x^2+4x)=-(-44x^2+34x)\)
11. \(-7x^2+9x=0\)
12. \(3(-7x^2-9x)=-(25x^2+20x)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(8x^2-12x=7x^2-2x \\ \Leftrightarrow x^2-10x=0 \\ \Leftrightarrow x(x-10) = 0 \\ \Leftrightarrow x = 0 \vee x-10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{10}{1} = 10 \\ V = \Big\{ 10; 0 \Big\} \\ -----------------\)
2. \(5x^2+5x=6x^2-10x \\ \Leftrightarrow -x^2+15x=0 \\ \Leftrightarrow x(-x+15) = 0 \\ \Leftrightarrow x = 0 \vee -x+15=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-15}{-1} = 15 \\ V = \Big\{ 15; 0 \Big\} \\ -----------------\)
3. \(9x^2+3x=6x^2+5x \\ \Leftrightarrow 3x^2-2x=0 \\ \Leftrightarrow x(3x-2) = 0 \\ \Leftrightarrow x = 0 \vee 3x-2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{2}{3} \\ V = \Big\{ \frac{2}{3}; 0 \Big\} \\ -----------------\)
4. \(-8x^2-12x=-3x^2+10x \\ \Leftrightarrow -5x^2-22x=0 \\ \Leftrightarrow x(-5x-22) = 0 \\ \Leftrightarrow x = 0 \vee -5x-22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{22}{-5} = \frac{-22}{5} \\ V = \Big\{ 0 ; \frac{-22}{5} \Big\} \\ -----------------\)
5. \(4x^2+8x=0 \\ \Leftrightarrow x(4x+8) = 0 \\ \Leftrightarrow x = 0 \vee 4x+8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-8}{4} = -2 \\ V = \Big\{ 0 ; -2 \Big\} \\ -----------------\)
6. \(-7x^2+15x=0 \\ \Leftrightarrow x(-7x+15) = 0 \\ \Leftrightarrow x = 0 \vee -7x+15=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-15}{-7} = \frac{15}{7} \\ V = \Big\{ \frac{15}{7}; 0 \Big\} \\ -----------------\)
7. \(x^2+15x=5x^2+6x \\ \Leftrightarrow -4x^2+9x=0 \\ \Leftrightarrow x(-4x+9) = 0 \\ \Leftrightarrow x = 0 \vee -4x+9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-9}{-4} = \frac{9}{4} \\ V = \Big\{ \frac{9}{4}; 0 \Big\} \\ -----------------\)
8. \(2(-5x^2+2x)=-(3x^2-14x) \\ \Leftrightarrow -10x^2+4x=-3x^2+14x \\ \Leftrightarrow -10x^2+4x+3x^2-14x= 0 \\ \Leftrightarrow -7x^2+10x=0 \\ \Leftrightarrow x(-7x+10) = 0 \\ \Leftrightarrow x = 0 \vee -7x+10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-10}{-7} = \frac{10}{7} \\ V = \Big\{ \frac{10}{7}; 0 \Big\} \\ -----------------\)
9. \(-5(-6x^2-6x)=-(-35x^2-9x) \\ \Leftrightarrow 30x^2+30x=35x^2+9x \\ \Leftrightarrow 30x^2+30x-35x^2-9x= 0 \\ \Leftrightarrow -5x^2-21x=0 \\ \Leftrightarrow x(-5x-21) = 0 \\ \Leftrightarrow x = 0 \vee -5x-21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{21}{-5} = \frac{-21}{5} \\ V = \Big\{ 0 ; \frac{-21}{5} \Big\} \\ -----------------\)
10. \(-5(-9x^2+4x)=-(-44x^2+34x) \\ \Leftrightarrow 45x^2-20x=44x^2-34x \\ \Leftrightarrow 45x^2-20x-44x^2+34x= 0 \\ \Leftrightarrow x^2-14x=0 \\ \Leftrightarrow x(x-14) = 0 \\ \Leftrightarrow x = 0 \vee x-14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{14}{1} = 14 \\ V = \Big\{ 14; 0 \Big\} \\ -----------------\)
11. \(-7x^2+9x=0 \\ \Leftrightarrow x(-7x+9) = 0 \\ \Leftrightarrow x = 0 \vee -7x+9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-9}{-7} = \frac{9}{7} \\ V = \Big\{ \frac{9}{7}; 0 \Big\} \\ -----------------\)
12. \(3(-7x^2-9x)=-(25x^2+20x) \\ \Leftrightarrow -21x^2-27x=-25x^2-20x \\ \Leftrightarrow -21x^2-27x+25x^2+20x= 0 \\ \Leftrightarrow 4x^2+7x=0 \\ \Leftrightarrow x(4x+7) = 0 \\ \Leftrightarrow x = 0 \vee 4x+7=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-7}{4} \\ V = \Big\{ 0 ; \frac{-7}{4} \Big\} \\ -----------------\)