Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(x^2+25x=0\)
2. \(4(-8x^2+10x)=-(37x^2-64x)\)
3. \(2(-8x^2+2x)=-(23x^2+18x)\)
4. \(-5(-2x^2-8x)=-(-16x^2-58x)\)
5. \(3(-4x^2+3x)=-(18x^2-11x)\)
6. \(3x^2-25x=5x^2-8x\)
7. \(-7x^2+14x=-4x^2-2x\)
8. \(-9x^2+15x=-4x^2-4x\)
9. \(-2x^2-5x=-4x^2+5x\)
10. \(3(9x^2-8x)=-(-29x^2+19x)\)
11. \(x^2+3x=0\)
12. \(-5x^2+22x=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(x^2+25x=0 \\ \Leftrightarrow x(x+25) = 0 \\ \Leftrightarrow x = 0 \vee x+25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-25}{1} = -25 \\ V = \Big\{ 0 ; -25 \Big\} \\ -----------------\)
2. \(4(-8x^2+10x)=-(37x^2-64x) \\ \Leftrightarrow -32x^2+40x=-37x^2+64x \\ \Leftrightarrow -32x^2+40x+37x^2-64x= 0 \\ \Leftrightarrow 5x^2+24x=0 \\ \Leftrightarrow x(5x+24) = 0 \\ \Leftrightarrow x = 0 \vee 5x+24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-24}{5} \\ V = \Big\{ 0 ; \frac{-24}{5} \Big\} \\ -----------------\)
3. \(2(-8x^2+2x)=-(23x^2+18x) \\ \Leftrightarrow -16x^2+4x=-23x^2-18x \\ \Leftrightarrow -16x^2+4x+23x^2+18x= 0 \\ \Leftrightarrow 7x^2-22x=0 \\ \Leftrightarrow x(7x-22) = 0 \\ \Leftrightarrow x = 0 \vee 7x-22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{22}{7} \\ V = \Big\{ \frac{22}{7}; 0 \Big\} \\ -----------------\)
4. \(-5(-2x^2-8x)=-(-16x^2-58x) \\ \Leftrightarrow 10x^2+40x=16x^2+58x \\ \Leftrightarrow 10x^2+40x-16x^2-58x= 0 \\ \Leftrightarrow -6x^2+18x=0 \\ \Leftrightarrow x(-6x+18) = 0 \\ \Leftrightarrow x = 0 \vee -6x+18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-18}{-6} = 3 \\ V = \Big\{ 3; 0 \Big\} \\ -----------------\)
5. \(3(-4x^2+3x)=-(18x^2-11x) \\ \Leftrightarrow -12x^2+9x=-18x^2+11x \\ \Leftrightarrow -12x^2+9x+18x^2-11x= 0 \\ \Leftrightarrow 6x^2+2x=0 \\ \Leftrightarrow x(6x+2) = 0 \\ \Leftrightarrow x = 0 \vee 6x+2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-2}{6} = \frac{-1}{3} \\ V = \Big\{ 0 ; \frac{-1}{3} \Big\} \\ -----------------\)
6. \(3x^2-25x=5x^2-8x \\ \Leftrightarrow -2x^2-17x=0 \\ \Leftrightarrow x(-2x-17) = 0 \\ \Leftrightarrow x = 0 \vee -2x-17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{17}{-2} = \frac{-17}{2} \\ V = \Big\{ 0 ; \frac{-17}{2} \Big\} \\ -----------------\)
7. \(-7x^2+14x=-4x^2-2x \\ \Leftrightarrow -3x^2+16x=0 \\ \Leftrightarrow x(-3x+16) = 0 \\ \Leftrightarrow x = 0 \vee -3x+16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-16}{-3} = \frac{16}{3} \\ V = \Big\{ \frac{16}{3}; 0 \Big\} \\ -----------------\)
8. \(-9x^2+15x=-4x^2-4x \\ \Leftrightarrow -5x^2+19x=0 \\ \Leftrightarrow x(-5x+19) = 0 \\ \Leftrightarrow x = 0 \vee -5x+19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-19}{-5} = \frac{19}{5} \\ V = \Big\{ \frac{19}{5}; 0 \Big\} \\ -----------------\)
9. \(-2x^2-5x=-4x^2+5x \\ \Leftrightarrow 2x^2-10x=0 \\ \Leftrightarrow x(2x-10) = 0 \\ \Leftrightarrow x = 0 \vee 2x-10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{10}{2} = 5 \\ V = \Big\{ 5; 0 \Big\} \\ -----------------\)
10. \(3(9x^2-8x)=-(-29x^2+19x) \\ \Leftrightarrow 27x^2-24x=29x^2-19x \\ \Leftrightarrow 27x^2-24x-29x^2+19x= 0 \\ \Leftrightarrow -2x^2+5x=0 \\ \Leftrightarrow x(-2x+5) = 0 \\ \Leftrightarrow x = 0 \vee -2x+5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-5}{-2} = \frac{5}{2} \\ V = \Big\{ \frac{5}{2}; 0 \Big\} \\ -----------------\)
11. \(x^2+3x=0 \\ \Leftrightarrow x(x+3) = 0 \\ \Leftrightarrow x = 0 \vee x+3=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-3}{1} = -3 \\ V = \Big\{ 0 ; -3 \Big\} \\ -----------------\)
12. \(-5x^2+22x=0 \\ \Leftrightarrow x(-5x+22) = 0 \\ \Leftrightarrow x = 0 \vee -5x+22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-22}{-5} = \frac{22}{5} \\ V = \Big\{ \frac{22}{5}; 0 \Big\} \\ -----------------\)