Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(10x^2-13x=6x^2-8x\)
2. \(-3(-7x^2+10x)=-(-24x^2+14x)\)
3. \(-2(-7x^2+6x)=-(-18x^2+30x)\)
4. \(x^2-16x=-2x^2+5x\)
5. \(-5(2x^2+10x)=-(16x^2+51x)\)
6. \(3(-9x^2+8x)=-(34x^2+x)\)
7. \(-8x^2+18x=0\)
8. \(-13x^2-33x=-7x^2-8x\)
9. \(-4(4x^2+10x)=-(10x^2+58x)\)
10. \(5(-10x^2+9x)=-(58x^2-58x)\)
11. \(-3x^2-13x=0\)
12. \(8x^2+2x=6x^2-7x\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(10x^2-13x=6x^2-8x \\ \Leftrightarrow 4x^2-5x=0 \\ \Leftrightarrow x(4x-5) = 0 \\ \Leftrightarrow x = 0 \vee 4x-5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{5}{4} \\ V = \Big\{ \frac{5}{4}; 0 \Big\} \\ -----------------\)
2. \(-3(-7x^2+10x)=-(-24x^2+14x) \\ \Leftrightarrow 21x^2-30x=24x^2-14x \\ \Leftrightarrow 21x^2-30x-24x^2+14x= 0 \\ \Leftrightarrow -3x^2+16x=0 \\ \Leftrightarrow x(-3x+16) = 0 \\ \Leftrightarrow x = 0 \vee -3x+16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-16}{-3} = \frac{16}{3} \\ V = \Big\{ \frac{16}{3}; 0 \Big\} \\ -----------------\)
3. \(-2(-7x^2+6x)=-(-18x^2+30x) \\ \Leftrightarrow 14x^2-12x=18x^2-30x \\ \Leftrightarrow 14x^2-12x-18x^2+30x= 0 \\ \Leftrightarrow -4x^2-18x=0 \\ \Leftrightarrow x(-4x-18) = 0 \\ \Leftrightarrow x = 0 \vee -4x-18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{18}{-4} = \frac{-9}{2} \\ V = \Big\{ 0 ; \frac{-9}{2} \Big\} \\ -----------------\)
4. \(x^2-16x=-2x^2+5x \\ \Leftrightarrow 3x^2-21x=0 \\ \Leftrightarrow x(3x-21) = 0 \\ \Leftrightarrow x = 0 \vee 3x-21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{21}{3} = 7 \\ V = \Big\{ 7; 0 \Big\} \\ -----------------\)
5. \(-5(2x^2+10x)=-(16x^2+51x) \\ \Leftrightarrow -10x^2-50x=-16x^2-51x \\ \Leftrightarrow -10x^2-50x+16x^2+51x= 0 \\ \Leftrightarrow 6x^2-1x=0 \\ \Leftrightarrow x(6x-1) = 0 \\ \Leftrightarrow x = 0 \vee 6x-1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{1}{6} \\ V = \Big\{ \frac{1}{6}; 0 \Big\} \\ -----------------\)
6. \(3(-9x^2+8x)=-(34x^2+x) \\ \Leftrightarrow -27x^2+24x=-34x^2-x \\ \Leftrightarrow -27x^2+24x+34x^2+x= 0 \\ \Leftrightarrow 7x^2-25x=0 \\ \Leftrightarrow x(7x-25) = 0 \\ \Leftrightarrow x = 0 \vee 7x-25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{25}{7} \\ V = \Big\{ \frac{25}{7}; 0 \Big\} \\ -----------------\)
7. \(-8x^2+18x=0 \\ \Leftrightarrow x(-8x+18) = 0 \\ \Leftrightarrow x = 0 \vee -8x+18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-18}{-8} = \frac{9}{4} \\ V = \Big\{ \frac{9}{4}; 0 \Big\} \\ -----------------\)
8. \(-13x^2-33x=-7x^2-8x \\ \Leftrightarrow -6x^2-25x=0 \\ \Leftrightarrow x(-6x-25) = 0 \\ \Leftrightarrow x = 0 \vee -6x-25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{25}{-6} = \frac{-25}{6} \\ V = \Big\{ 0 ; \frac{-25}{6} \Big\} \\ -----------------\)
9. \(-4(4x^2+10x)=-(10x^2+58x) \\ \Leftrightarrow -16x^2-40x=-10x^2-58x \\ \Leftrightarrow -16x^2-40x+10x^2+58x= 0 \\ \Leftrightarrow -6x^2-18x=0 \\ \Leftrightarrow x(-6x-18) = 0 \\ \Leftrightarrow x = 0 \vee -6x-18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{18}{-6} = -3 \\ V = \Big\{ 0 ; -3 \Big\} \\ -----------------\)
10. \(5(-10x^2+9x)=-(58x^2-58x) \\ \Leftrightarrow -50x^2+45x=-58x^2+58x \\ \Leftrightarrow -50x^2+45x+58x^2-58x= 0 \\ \Leftrightarrow 8x^2+13x=0 \\ \Leftrightarrow x(8x+13) = 0 \\ \Leftrightarrow x = 0 \vee 8x+13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-13}{8} \\ V = \Big\{ 0 ; \frac{-13}{8} \Big\} \\ -----------------\)
11. \(-3x^2-13x=0 \\ \Leftrightarrow x(-3x-13) = 0 \\ \Leftrightarrow x = 0 \vee -3x-13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{13}{-3} = \frac{-13}{3} \\ V = \Big\{ 0 ; \frac{-13}{3} \Big\} \\ -----------------\)
12. \(8x^2+2x=6x^2-7x \\ \Leftrightarrow 2x^2+9x=0 \\ \Leftrightarrow x(2x+9) = 0 \\ \Leftrightarrow x = 0 \vee 2x+9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-9}{2} \\ V = \Big\{ 0 ; \frac{-9}{2} \Big\} \\ -----------------\)