Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-2(-8x^2-9x)=-(-19x^2-19x)\)
2. \(10x^2+19x=4x^2+8x\)
3. \(-4(-5x^2+10x)=-(-13x^2+38x)\)
4. \(-5x^2-15x=0\)
5. \(11x^2+23x=5x^2+9x\)
6. \(-12x^2-8x=-7x^2-9x\)
7. \(6x^2-6x=9x^2+7x\)
8. \(2x^2-1x=0\)
9. \(5x^2+15x=2x^2-2x\)
10. \(5x^2+24x=0\)
11. \(-3x^2-30x=-10x^2-5x\)
12. \(-3(-9x^2+10x)=-(-22x^2+27x)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-2(-8x^2-9x)=-(-19x^2-19x) \\ \Leftrightarrow 16x^2+18x=19x^2+19x \\ \Leftrightarrow 16x^2+18x-19x^2-19x= 0 \\ \Leftrightarrow -3x^2+1x=0 \\ \Leftrightarrow x(-3x+1) = 0 \\ \Leftrightarrow x = 0 \vee -3x+1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-1}{-3} = \frac{1}{3} \\ V = \Big\{ \frac{1}{3}; 0 \Big\} \\ -----------------\)
2. \(10x^2+19x=4x^2+8x \\ \Leftrightarrow 6x^2+11x=0 \\ \Leftrightarrow x(6x+11) = 0 \\ \Leftrightarrow x = 0 \vee 6x+11=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-11}{6} \\ V = \Big\{ 0 ; \frac{-11}{6} \Big\} \\ -----------------\)
3. \(-4(-5x^2+10x)=-(-13x^2+38x) \\ \Leftrightarrow 20x^2-40x=13x^2-38x \\ \Leftrightarrow 20x^2-40x-13x^2+38x= 0 \\ \Leftrightarrow 7x^2+2x=0 \\ \Leftrightarrow x(7x+2) = 0 \\ \Leftrightarrow x = 0 \vee 7x+2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-2}{7} \\ V = \Big\{ 0 ; \frac{-2}{7} \Big\} \\ -----------------\)
4. \(-5x^2-15x=0 \\ \Leftrightarrow x(-5x-15) = 0 \\ \Leftrightarrow x = 0 \vee -5x-15=0 \\ \Leftrightarrow x = 0 \vee x = \frac{15}{-5} = -3 \\ V = \Big\{ 0 ; -3 \Big\} \\ -----------------\)
5. \(11x^2+23x=5x^2+9x \\ \Leftrightarrow 6x^2+14x=0 \\ \Leftrightarrow x(6x+14) = 0 \\ \Leftrightarrow x = 0 \vee 6x+14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-14}{6} = \frac{-7}{3} \\ V = \Big\{ 0 ; \frac{-7}{3} \Big\} \\ -----------------\)
6. \(-12x^2-8x=-7x^2-9x \\ \Leftrightarrow -5x^2+1x=0 \\ \Leftrightarrow x(-5x+1) = 0 \\ \Leftrightarrow x = 0 \vee -5x+1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-1}{-5} = \frac{1}{5} \\ V = \Big\{ \frac{1}{5}; 0 \Big\} \\ -----------------\)
7. \(6x^2-6x=9x^2+7x \\ \Leftrightarrow -3x^2-13x=0 \\ \Leftrightarrow x(-3x-13) = 0 \\ \Leftrightarrow x = 0 \vee -3x-13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{13}{-3} = \frac{-13}{3} \\ V = \Big\{ 0 ; \frac{-13}{3} \Big\} \\ -----------------\)
8. \(2x^2-1x=0 \\ \Leftrightarrow x(2x-1) = 0 \\ \Leftrightarrow x = 0 \vee 2x-1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{1}{2} \\ V = \Big\{ \frac{1}{2}; 0 \Big\} \\ -----------------\)
9. \(5x^2+15x=2x^2-2x \\ \Leftrightarrow 3x^2+17x=0 \\ \Leftrightarrow x(3x+17) = 0 \\ \Leftrightarrow x = 0 \vee 3x+17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-17}{3} \\ V = \Big\{ 0 ; \frac{-17}{3} \Big\} \\ -----------------\)
10. \(5x^2+24x=0 \\ \Leftrightarrow x(5x+24) = 0 \\ \Leftrightarrow x = 0 \vee 5x+24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-24}{5} \\ V = \Big\{ 0 ; \frac{-24}{5} \Big\} \\ -----------------\)
11. \(-3x^2-30x=-10x^2-5x \\ \Leftrightarrow 7x^2-25x=0 \\ \Leftrightarrow x(7x-25) = 0 \\ \Leftrightarrow x = 0 \vee 7x-25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{25}{7} \\ V = \Big\{ \frac{25}{7}; 0 \Big\} \\ -----------------\)
12. \(-3(-9x^2+10x)=-(-22x^2+27x) \\ \Leftrightarrow 27x^2-30x=22x^2-27x \\ \Leftrightarrow 27x^2-30x-22x^2+27x= 0 \\ \Leftrightarrow 5x^2+3x=0 \\ \Leftrightarrow x(5x+3) = 0 \\ \Leftrightarrow x = 0 \vee 5x+3=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-3}{5} \\ V = \Big\{ 0 ; \frac{-3}{5} \Big\} \\ -----------------\)