Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-5(10x^2+4x)=-(44x^2+3x)\)
2. \(10x^2+2x=6x^2+4x\)
3. \(x^2+21x=-4x^2-2x\)
4. \(-5(3x^2+9x)=-(11x^2+50x)\)
5. \(-4(6x^2+4x)=-(19x^2+19x)\)
6. \(2(-7x^2-10x)=-(10x^2+43x)\)
7. \(-6x^2-23x=-7x^2+2x\)
8. \(-14x^2-6x=-9x^2-7x\)
9. \(x^2-15x=0\)
10. \(3(-5x^2-9x)=-(21x^2+47x)\)
11. \(10x^2-10x=2x^2-3x\)
12. \(9x^2+8x=5x^2-2x\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-5(10x^2+4x)=-(44x^2+3x) \\ \Leftrightarrow -50x^2-20x=-44x^2-3x \\ \Leftrightarrow -50x^2-20x+44x^2+3x= 0 \\ \Leftrightarrow -6x^2+17x=0 \\ \Leftrightarrow x(-6x+17) = 0 \\ \Leftrightarrow x = 0 \vee -6x+17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-17}{-6} = \frac{17}{6} \\ V = \Big\{ \frac{17}{6}; 0 \Big\} \\ -----------------\)
2. \(10x^2+2x=6x^2+4x \\ \Leftrightarrow 4x^2-2x=0 \\ \Leftrightarrow x(4x-2) = 0 \\ \Leftrightarrow x = 0 \vee 4x-2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{2}{4} = \frac{1}{2} \\ V = \Big\{ \frac{1}{2}; 0 \Big\} \\ -----------------\)
3. \(x^2+21x=-4x^2-2x \\ \Leftrightarrow 5x^2+23x=0 \\ \Leftrightarrow x(5x+23) = 0 \\ \Leftrightarrow x = 0 \vee 5x+23=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-23}{5} \\ V = \Big\{ 0 ; \frac{-23}{5} \Big\} \\ -----------------\)
4. \(-5(3x^2+9x)=-(11x^2+50x) \\ \Leftrightarrow -15x^2-45x=-11x^2-50x \\ \Leftrightarrow -15x^2-45x+11x^2+50x= 0 \\ \Leftrightarrow -4x^2-5x=0 \\ \Leftrightarrow x(-4x-5) = 0 \\ \Leftrightarrow x = 0 \vee -4x-5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{5}{-4} = \frac{-5}{4} \\ V = \Big\{ 0 ; \frac{-5}{4} \Big\} \\ -----------------\)
5. \(-4(6x^2+4x)=-(19x^2+19x) \\ \Leftrightarrow -24x^2-16x=-19x^2-19x \\ \Leftrightarrow -24x^2-16x+19x^2+19x= 0 \\ \Leftrightarrow -5x^2-3x=0 \\ \Leftrightarrow x(-5x-3) = 0 \\ \Leftrightarrow x = 0 \vee -5x-3=0 \\ \Leftrightarrow x = 0 \vee x = \frac{3}{-5} = \frac{-3}{5} \\ V = \Big\{ 0 ; \frac{-3}{5} \Big\} \\ -----------------\)
6. \(2(-7x^2-10x)=-(10x^2+43x) \\ \Leftrightarrow -14x^2-20x=-10x^2-43x \\ \Leftrightarrow -14x^2-20x+10x^2+43x= 0 \\ \Leftrightarrow -4x^2-23x=0 \\ \Leftrightarrow x(-4x-23) = 0 \\ \Leftrightarrow x = 0 \vee -4x-23=0 \\ \Leftrightarrow x = 0 \vee x = \frac{23}{-4} = \frac{-23}{4} \\ V = \Big\{ 0 ; \frac{-23}{4} \Big\} \\ -----------------\)
7. \(-6x^2-23x=-7x^2+2x \\ \Leftrightarrow x^2-25x=0 \\ \Leftrightarrow x(x-25) = 0 \\ \Leftrightarrow x = 0 \vee x-25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{25}{1} = 25 \\ V = \Big\{ 25; 0 \Big\} \\ -----------------\)
8. \(-14x^2-6x=-9x^2-7x \\ \Leftrightarrow -5x^2+1x=0 \\ \Leftrightarrow x(-5x+1) = 0 \\ \Leftrightarrow x = 0 \vee -5x+1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-1}{-5} = \frac{1}{5} \\ V = \Big\{ \frac{1}{5}; 0 \Big\} \\ -----------------\)
9. \(x^2-15x=0 \\ \Leftrightarrow x(x-15) = 0 \\ \Leftrightarrow x = 0 \vee x-15=0 \\ \Leftrightarrow x = 0 \vee x = \frac{15}{1} = 15 \\ V = \Big\{ 15; 0 \Big\} \\ -----------------\)
10. \(3(-5x^2-9x)=-(21x^2+47x) \\ \Leftrightarrow -15x^2-27x=-21x^2-47x \\ \Leftrightarrow -15x^2-27x+21x^2+47x= 0 \\ \Leftrightarrow 6x^2-20x=0 \\ \Leftrightarrow x(6x-20) = 0 \\ \Leftrightarrow x = 0 \vee 6x-20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{20}{6} = \frac{10}{3} \\ V = \Big\{ \frac{10}{3}; 0 \Big\} \\ -----------------\)
11. \(10x^2-10x=2x^2-3x \\ \Leftrightarrow 8x^2-7x=0 \\ \Leftrightarrow x(8x-7) = 0 \\ \Leftrightarrow x = 0 \vee 8x-7=0 \\ \Leftrightarrow x = 0 \vee x = \frac{7}{8} \\ V = \Big\{ \frac{7}{8}; 0 \Big\} \\ -----------------\)
12. \(9x^2+8x=5x^2-2x \\ \Leftrightarrow 4x^2+10x=0 \\ \Leftrightarrow x(4x+10) = 0 \\ \Leftrightarrow x = 0 \vee 4x+10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-10}{4} = \frac{-5}{2} \\ V = \Big\{ 0 ; \frac{-5}{2} \Big\} \\ -----------------\)