Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-3x^2-10x=4x^2+4x\)
2. \(-6x^2-12x=-5x^2+7x\)
3. \(2(4x^2-3x)=-(-14x^2+26x)\)
4. \(-2(9x^2+2x)=-(10x^2-21x)\)
5. \(-8x^2+12x=0\)
6. \(-5x^2+19x=0\)
7. \(-3x^2-16x=0\)
8. \(-4(6x^2-4x)=-(25x^2-40x)\)
9. \(4(-2x^2-8x)=-(9x^2+37x)\)
10. \(4x^2-33x=-4x^2-9x\)
11. \(-2(3x^2+5x)=-(-2x^2+27x)\)
12. \(-2(-6x^2+4x)=-(-17x^2+7x)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-3x^2-10x=4x^2+4x \\ \Leftrightarrow -7x^2-14x=0 \\ \Leftrightarrow x(-7x-14) = 0 \\ \Leftrightarrow x = 0 \vee -7x-14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{14}{-7} = -2 \\ V = \Big\{ 0 ; -2 \Big\} \\ -----------------\)
2. \(-6x^2-12x=-5x^2+7x \\ \Leftrightarrow -x^2-19x=0 \\ \Leftrightarrow x(-x-19) = 0 \\ \Leftrightarrow x = 0 \vee -x-19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{19}{-1} = -19 \\ V = \Big\{ 0 ; -19 \Big\} \\ -----------------\)
3. \(2(4x^2-3x)=-(-14x^2+26x) \\ \Leftrightarrow 8x^2-6x=14x^2-26x \\ \Leftrightarrow 8x^2-6x-14x^2+26x= 0 \\ \Leftrightarrow -6x^2-20x=0 \\ \Leftrightarrow x(-6x-20) = 0 \\ \Leftrightarrow x = 0 \vee -6x-20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{20}{-6} = \frac{-10}{3} \\ V = \Big\{ 0 ; \frac{-10}{3} \Big\} \\ -----------------\)
4. \(-2(9x^2+2x)=-(10x^2-21x) \\ \Leftrightarrow -18x^2-4x=-10x^2+21x \\ \Leftrightarrow -18x^2-4x+10x^2-21x= 0 \\ \Leftrightarrow -8x^2+25x=0 \\ \Leftrightarrow x(-8x+25) = 0 \\ \Leftrightarrow x = 0 \vee -8x+25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-25}{-8} = \frac{25}{8} \\ V = \Big\{ \frac{25}{8}; 0 \Big\} \\ -----------------\)
5. \(-8x^2+12x=0 \\ \Leftrightarrow x(-8x+12) = 0 \\ \Leftrightarrow x = 0 \vee -8x+12=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-12}{-8} = \frac{3}{2} \\ V = \Big\{ \frac{3}{2}; 0 \Big\} \\ -----------------\)
6. \(-5x^2+19x=0 \\ \Leftrightarrow x(-5x+19) = 0 \\ \Leftrightarrow x = 0 \vee -5x+19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-19}{-5} = \frac{19}{5} \\ V = \Big\{ \frac{19}{5}; 0 \Big\} \\ -----------------\)
7. \(-3x^2-16x=0 \\ \Leftrightarrow x(-3x-16) = 0 \\ \Leftrightarrow x = 0 \vee -3x-16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{16}{-3} = \frac{-16}{3} \\ V = \Big\{ 0 ; \frac{-16}{3} \Big\} \\ -----------------\)
8. \(-4(6x^2-4x)=-(25x^2-40x) \\ \Leftrightarrow -24x^2+16x=-25x^2+40x \\ \Leftrightarrow -24x^2+16x+25x^2-40x= 0 \\ \Leftrightarrow x^2+24x=0 \\ \Leftrightarrow x(x+24) = 0 \\ \Leftrightarrow x = 0 \vee x+24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-24}{1} = -24 \\ V = \Big\{ 0 ; -24 \Big\} \\ -----------------\)
9. \(4(-2x^2-8x)=-(9x^2+37x) \\ \Leftrightarrow -8x^2-32x=-9x^2-37x \\ \Leftrightarrow -8x^2-32x+9x^2+37x= 0 \\ \Leftrightarrow x^2-5x=0 \\ \Leftrightarrow x(x-5) = 0 \\ \Leftrightarrow x = 0 \vee x-5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{5}{1} = 5 \\ V = \Big\{ 5; 0 \Big\} \\ -----------------\)
10. \(4x^2-33x=-4x^2-9x \\ \Leftrightarrow 8x^2-24x=0 \\ \Leftrightarrow x(8x-24) = 0 \\ \Leftrightarrow x = 0 \vee 8x-24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{24}{8} = 3 \\ V = \Big\{ 3; 0 \Big\} \\ -----------------\)
11. \(-2(3x^2+5x)=-(-2x^2+27x) \\ \Leftrightarrow -6x^2-10x=2x^2-27x \\ \Leftrightarrow -6x^2-10x-2x^2+27x= 0 \\ \Leftrightarrow -8x^2-17x=0 \\ \Leftrightarrow x(-8x-17) = 0 \\ \Leftrightarrow x = 0 \vee -8x-17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{17}{-8} = \frac{-17}{8} \\ V = \Big\{ 0 ; \frac{-17}{8} \Big\} \\ -----------------\)
12. \(-2(-6x^2+4x)=-(-17x^2+7x) \\ \Leftrightarrow 12x^2-8x=17x^2-7x \\ \Leftrightarrow 12x^2-8x-17x^2+7x= 0 \\ \Leftrightarrow -5x^2+1x=0 \\ \Leftrightarrow x(-5x+1) = 0 \\ \Leftrightarrow x = 0 \vee -5x+1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-1}{-5} = \frac{1}{5} \\ V = \Big\{ \frac{1}{5}; 0 \Big\} \\ -----------------\)