Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(5x^2+6x=0\)
2. \(-8x^2-23x=0\)
3. \(-x^2-8x=0\)
4. \(10x^2+14x=7x^2+10x\)
5. \(12x^2+13x=8x^2-9x\)
6. \(x^2-7x=0\)
7. \(x^2+19x=2x^2+9x\)
8. \(7x^2-24x=0\)
9. \(-3(-2x^2+3x)=-(-14x^2+15x)\)
10. \(3(-9x^2-5x)=-(25x^2+30x)\)
11. \(-5(9x^2+3x)=-(43x^2+36x)\)
12. \(2(7x^2+5x)=-(-11x^2+0x)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(5x^2+6x=0 \\ \Leftrightarrow x(5x+6) = 0 \\ \Leftrightarrow x = 0 \vee 5x+6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-6}{5} \\ V = \Big\{ 0 ; \frac{-6}{5} \Big\} \\ -----------------\)
2. \(-8x^2-23x=0 \\ \Leftrightarrow x(-8x-23) = 0 \\ \Leftrightarrow x = 0 \vee -8x-23=0 \\ \Leftrightarrow x = 0 \vee x = \frac{23}{-8} = \frac{-23}{8} \\ V = \Big\{ 0 ; \frac{-23}{8} \Big\} \\ -----------------\)
3. \(-x^2-8x=0 \\ \Leftrightarrow x(-x-8) = 0 \\ \Leftrightarrow x = 0 \vee -x-8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{8}{-1} = -8 \\ V = \Big\{ 0 ; -8 \Big\} \\ -----------------\)
4. \(10x^2+14x=7x^2+10x \\ \Leftrightarrow 3x^2+4x=0 \\ \Leftrightarrow x(3x+4) = 0 \\ \Leftrightarrow x = 0 \vee 3x+4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-4}{3} \\ V = \Big\{ 0 ; \frac{-4}{3} \Big\} \\ -----------------\)
5. \(12x^2+13x=8x^2-9x \\ \Leftrightarrow 4x^2+22x=0 \\ \Leftrightarrow x(4x+22) = 0 \\ \Leftrightarrow x = 0 \vee 4x+22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-22}{4} = \frac{-11}{2} \\ V = \Big\{ 0 ; \frac{-11}{2} \Big\} \\ -----------------\)
6. \(x^2-7x=0 \\ \Leftrightarrow x(x-7) = 0 \\ \Leftrightarrow x = 0 \vee x-7=0 \\ \Leftrightarrow x = 0 \vee x = \frac{7}{1} = 7 \\ V = \Big\{ 7; 0 \Big\} \\ -----------------\)
7. \(x^2+19x=2x^2+9x \\ \Leftrightarrow -x^2+10x=0 \\ \Leftrightarrow x(-x+10) = 0 \\ \Leftrightarrow x = 0 \vee -x+10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-10}{-1} = 10 \\ V = \Big\{ 10; 0 \Big\} \\ -----------------\)
8. \(7x^2-24x=0 \\ \Leftrightarrow x(7x-24) = 0 \\ \Leftrightarrow x = 0 \vee 7x-24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{24}{7} \\ V = \Big\{ \frac{24}{7}; 0 \Big\} \\ -----------------\)
9. \(-3(-2x^2+3x)=-(-14x^2+15x) \\ \Leftrightarrow 6x^2-9x=14x^2-15x \\ \Leftrightarrow 6x^2-9x-14x^2+15x= 0 \\ \Leftrightarrow -8x^2-6x=0 \\ \Leftrightarrow x(-8x-6) = 0 \\ \Leftrightarrow x = 0 \vee -8x-6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{6}{-8} = \frac{-3}{4} \\ V = \Big\{ 0 ; \frac{-3}{4} \Big\} \\ -----------------\)
10. \(3(-9x^2-5x)=-(25x^2+30x) \\ \Leftrightarrow -27x^2-15x=-25x^2-30x \\ \Leftrightarrow -27x^2-15x+25x^2+30x= 0 \\ \Leftrightarrow -2x^2-15x=0 \\ \Leftrightarrow x(-2x-15) = 0 \\ \Leftrightarrow x = 0 \vee -2x-15=0 \\ \Leftrightarrow x = 0 \vee x = \frac{15}{-2} = \frac{-15}{2} \\ V = \Big\{ 0 ; \frac{-15}{2} \Big\} \\ -----------------\)
11. \(-5(9x^2+3x)=-(43x^2+36x) \\ \Leftrightarrow -45x^2-15x=-43x^2-36x \\ \Leftrightarrow -45x^2-15x+43x^2+36x= 0 \\ \Leftrightarrow -2x^2-21x=0 \\ \Leftrightarrow x(-2x-21) = 0 \\ \Leftrightarrow x = 0 \vee -2x-21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{21}{-2} = \frac{-21}{2} \\ V = \Big\{ 0 ; \frac{-21}{2} \Big\} \\ -----------------\)
12. \(2(7x^2+5x)=-(-11x^2+0x) \\ \Leftrightarrow 14x^2+10x=11x^2+0x \\ \Leftrightarrow 14x^2+10x-11x^2+0x= 0 \\ \Leftrightarrow 3x^2-10x=0 \\ \Leftrightarrow x(3x-10) = 0 \\ \Leftrightarrow x = 0 \vee 3x-10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{10}{3} \\ V = \Big\{ \frac{10}{3}; 0 \Big\} \\ -----------------\)