Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(5(10x^2-3x)=-(-53x^2-7x)\)
2. \(-12x^2-6x=-10x^2-8x\)
3. \(15x^2-20x=10x^2+2x\)
4. \(x^2-10x=8x^2-9x\)
5. \(5x^2-18x=0\)
6. \(2(-6x^2+10x)=-(7x^2+4x)\)
7. \(4(9x^2+2x)=-(-31x^2+8x)\)
8. \(5(-6x^2+8x)=-(22x^2-49x)\)
9. \(13x^2+17x=9x^2+2x\)
10. \(6x^2-23x=0\)
11. \(-x^2-7x=0\)
12. \(x^2+4x=3x^2+6x\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(5(10x^2-3x)=-(-53x^2-7x) \\ \Leftrightarrow 50x^2-15x=53x^2+7x \\ \Leftrightarrow 50x^2-15x-53x^2-7x= 0 \\ \Leftrightarrow -3x^2+22x=0 \\ \Leftrightarrow x(-3x+22) = 0 \\ \Leftrightarrow x = 0 \vee -3x+22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-22}{-3} = \frac{22}{3} \\ V = \Big\{ \frac{22}{3}; 0 \Big\} \\ -----------------\)
2. \(-12x^2-6x=-10x^2-8x \\ \Leftrightarrow -2x^2+2x=0 \\ \Leftrightarrow x(-2x+2) = 0 \\ \Leftrightarrow x = 0 \vee -2x+2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-2}{-2} = 1 \\ V = \Big\{ 1; 0 \Big\} \\ -----------------\)
3. \(15x^2-20x=10x^2+2x \\ \Leftrightarrow 5x^2-22x=0 \\ \Leftrightarrow x(5x-22) = 0 \\ \Leftrightarrow x = 0 \vee 5x-22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{22}{5} \\ V = \Big\{ \frac{22}{5}; 0 \Big\} \\ -----------------\)
4. \(x^2-10x=8x^2-9x \\ \Leftrightarrow -7x^2-1x=0 \\ \Leftrightarrow x(-7x-1) = 0 \\ \Leftrightarrow x = 0 \vee -7x-1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{1}{-7} = \frac{-1}{7} \\ V = \Big\{ 0 ; \frac{-1}{7} \Big\} \\ -----------------\)
5. \(5x^2-18x=0 \\ \Leftrightarrow x(5x-18) = 0 \\ \Leftrightarrow x = 0 \vee 5x-18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{18}{5} \\ V = \Big\{ \frac{18}{5}; 0 \Big\} \\ -----------------\)
6. \(2(-6x^2+10x)=-(7x^2+4x) \\ \Leftrightarrow -12x^2+20x=-7x^2-4x \\ \Leftrightarrow -12x^2+20x+7x^2+4x= 0 \\ \Leftrightarrow -5x^2-24x=0 \\ \Leftrightarrow x(-5x-24) = 0 \\ \Leftrightarrow x = 0 \vee -5x-24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{24}{-5} = \frac{-24}{5} \\ V = \Big\{ 0 ; \frac{-24}{5} \Big\} \\ -----------------\)
7. \(4(9x^2+2x)=-(-31x^2+8x) \\ \Leftrightarrow 36x^2+8x=31x^2-8x \\ \Leftrightarrow 36x^2+8x-31x^2+8x= 0 \\ \Leftrightarrow 5x^2-16x=0 \\ \Leftrightarrow x(5x-16) = 0 \\ \Leftrightarrow x = 0 \vee 5x-16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{16}{5} \\ V = \Big\{ \frac{16}{5}; 0 \Big\} \\ -----------------\)
8. \(5(-6x^2+8x)=-(22x^2-49x) \\ \Leftrightarrow -30x^2+40x=-22x^2+49x \\ \Leftrightarrow -30x^2+40x+22x^2-49x= 0 \\ \Leftrightarrow -8x^2+9x=0 \\ \Leftrightarrow x(-8x+9) = 0 \\ \Leftrightarrow x = 0 \vee -8x+9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-9}{-8} = \frac{9}{8} \\ V = \Big\{ \frac{9}{8}; 0 \Big\} \\ -----------------\)
9. \(13x^2+17x=9x^2+2x \\ \Leftrightarrow 4x^2+15x=0 \\ \Leftrightarrow x(4x+15) = 0 \\ \Leftrightarrow x = 0 \vee 4x+15=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-15}{4} \\ V = \Big\{ 0 ; \frac{-15}{4} \Big\} \\ -----------------\)
10. \(6x^2-23x=0 \\ \Leftrightarrow x(6x-23) = 0 \\ \Leftrightarrow x = 0 \vee 6x-23=0 \\ \Leftrightarrow x = 0 \vee x = \frac{23}{6} \\ V = \Big\{ \frac{23}{6}; 0 \Big\} \\ -----------------\)
11. \(-x^2-7x=0 \\ \Leftrightarrow x(-x-7) = 0 \\ \Leftrightarrow x = 0 \vee -x-7=0 \\ \Leftrightarrow x = 0 \vee x = \frac{7}{-1} = -7 \\ V = \Big\{ 0 ; -7 \Big\} \\ -----------------\)
12. \(x^2+4x=3x^2+6x \\ \Leftrightarrow -2x^2-2x=0 \\ \Leftrightarrow x(-2x-2) = 0 \\ \Leftrightarrow x = 0 \vee -2x-2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{2}{-2} = -1 \\ V = \Big\{ 0 ; -1 \Big\} \\ -----------------\)