Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(x^2+3x=-4x^2-10x\)
2. \(-7x^2+10x=0\)
3. \(10x^2-29x=8x^2-8x\)
4. \(-2(-8x^2-5x)=-(-19x^2-29x)\)
5. \(-5(-6x^2-8x)=-(-33x^2-39x)\)
6. \(5(-6x^2+5x)=-(31x^2-29x)\)
7. \(-2(2x^2+8x)=-(-2x^2+11x)\)
8. \(-3x^2+8x=-8x^2-6x\)
9. \(-4(-10x^2-9x)=-(-41x^2-25x)\)
10. \(-x^2-10x=0\)
11. \(-x^2-14x=-8x^2+2x\)
12. \(-4(-10x^2+9x)=-(-44x^2+32x)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(x^2+3x=-4x^2-10x \\ \Leftrightarrow 5x^2+13x=0 \\ \Leftrightarrow x(5x+13) = 0 \\ \Leftrightarrow x = 0 \vee 5x+13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-13}{5} \\ V = \Big\{ 0 ; \frac{-13}{5} \Big\} \\ -----------------\)
2. \(-7x^2+10x=0 \\ \Leftrightarrow x(-7x+10) = 0 \\ \Leftrightarrow x = 0 \vee -7x+10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-10}{-7} = \frac{10}{7} \\ V = \Big\{ \frac{10}{7}; 0 \Big\} \\ -----------------\)
3. \(10x^2-29x=8x^2-8x \\ \Leftrightarrow 2x^2-21x=0 \\ \Leftrightarrow x(2x-21) = 0 \\ \Leftrightarrow x = 0 \vee 2x-21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{21}{2} \\ V = \Big\{ \frac{21}{2}; 0 \Big\} \\ -----------------\)
4. \(-2(-8x^2-5x)=-(-19x^2-29x) \\ \Leftrightarrow 16x^2+10x=19x^2+29x \\ \Leftrightarrow 16x^2+10x-19x^2-29x= 0 \\ \Leftrightarrow -3x^2+19x=0 \\ \Leftrightarrow x(-3x+19) = 0 \\ \Leftrightarrow x = 0 \vee -3x+19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-19}{-3} = \frac{19}{3} \\ V = \Big\{ \frac{19}{3}; 0 \Big\} \\ -----------------\)
5. \(-5(-6x^2-8x)=-(-33x^2-39x) \\ \Leftrightarrow 30x^2+40x=33x^2+39x \\ \Leftrightarrow 30x^2+40x-33x^2-39x= 0 \\ \Leftrightarrow -3x^2-1x=0 \\ \Leftrightarrow x(-3x-1) = 0 \\ \Leftrightarrow x = 0 \vee -3x-1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{1}{-3} = \frac{-1}{3} \\ V = \Big\{ 0 ; \frac{-1}{3} \Big\} \\ -----------------\)
6. \(5(-6x^2+5x)=-(31x^2-29x) \\ \Leftrightarrow -30x^2+25x=-31x^2+29x \\ \Leftrightarrow -30x^2+25x+31x^2-29x= 0 \\ \Leftrightarrow x^2+4x=0 \\ \Leftrightarrow x(x+4) = 0 \\ \Leftrightarrow x = 0 \vee x+4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-4}{1} = -4 \\ V = \Big\{ 0 ; -4 \Big\} \\ -----------------\)
7. \(-2(2x^2+8x)=-(-2x^2+11x) \\ \Leftrightarrow -4x^2-16x=2x^2-11x \\ \Leftrightarrow -4x^2-16x-2x^2+11x= 0 \\ \Leftrightarrow -6x^2+5x=0 \\ \Leftrightarrow x(-6x+5) = 0 \\ \Leftrightarrow x = 0 \vee -6x+5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-5}{-6} = \frac{5}{6} \\ V = \Big\{ \frac{5}{6}; 0 \Big\} \\ -----------------\)
8. \(-3x^2+8x=-8x^2-6x \\ \Leftrightarrow 5x^2+14x=0 \\ \Leftrightarrow x(5x+14) = 0 \\ \Leftrightarrow x = 0 \vee 5x+14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-14}{5} \\ V = \Big\{ 0 ; \frac{-14}{5} \Big\} \\ -----------------\)
9. \(-4(-10x^2-9x)=-(-41x^2-25x) \\ \Leftrightarrow 40x^2+36x=41x^2+25x \\ \Leftrightarrow 40x^2+36x-41x^2-25x= 0 \\ \Leftrightarrow -x^2-11x=0 \\ \Leftrightarrow x(-x-11) = 0 \\ \Leftrightarrow x = 0 \vee -x-11=0 \\ \Leftrightarrow x = 0 \vee x = \frac{11}{-1} = -11 \\ V = \Big\{ 0 ; -11 \Big\} \\ -----------------\)
10. \(-x^2-10x=0 \\ \Leftrightarrow x(-x-10) = 0 \\ \Leftrightarrow x = 0 \vee -x-10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{10}{-1} = -10 \\ V = \Big\{ 0 ; -10 \Big\} \\ -----------------\)
11. \(-x^2-14x=-8x^2+2x \\ \Leftrightarrow 7x^2-16x=0 \\ \Leftrightarrow x(7x-16) = 0 \\ \Leftrightarrow x = 0 \vee 7x-16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{16}{7} \\ V = \Big\{ \frac{16}{7}; 0 \Big\} \\ -----------------\)
12. \(-4(-10x^2+9x)=-(-44x^2+32x) \\ \Leftrightarrow 40x^2-36x=44x^2-32x \\ \Leftrightarrow 40x^2-36x-44x^2+32x= 0 \\ \Leftrightarrow -4x^2+4x=0 \\ \Leftrightarrow x(-4x+4) = 0 \\ \Leftrightarrow x = 0 \vee -4x+4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-4}{-4} = 1 \\ V = \Big\{ 1; 0 \Big\} \\ -----------------\)