Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(4(-6x^2-3x)=-(32x^2+30x)\)
2. \(-7x^2-10x=-8x^2+6x\)
3. \(4x^2+20x=9x^2+9x\)
4. \(-4x^2-9x=-10x^2-5x\)
5. \(4(-2x^2+8x)=-(14x^2-29x)\)
6. \(-8x^2+8x=0\)
7. \(-x^2+11x=-6x^2+10x\)
8. \(13x^2+27x=8x^2+8x\)
9. \(6x^2+9x=0\)
10. \(-4x^2+5x=0\)
11. \(-2(-9x^2-7x)=-(-20x^2-2x)\)
12. \(13x^2-8x=9x^2+7x\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(4(-6x^2-3x)=-(32x^2+30x) \\ \Leftrightarrow -24x^2-12x=-32x^2-30x \\ \Leftrightarrow -24x^2-12x+32x^2+30x= 0 \\ \Leftrightarrow 8x^2-18x=0 \\ \Leftrightarrow x(8x-18) = 0 \\ \Leftrightarrow x = 0 \vee 8x-18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{18}{8} = \frac{9}{4} \\ V = \Big\{ \frac{9}{4}; 0 \Big\} \\ -----------------\)
2. \(-7x^2-10x=-8x^2+6x \\ \Leftrightarrow x^2-16x=0 \\ \Leftrightarrow x(x-16) = 0 \\ \Leftrightarrow x = 0 \vee x-16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{16}{1} = 16 \\ V = \Big\{ 16; 0 \Big\} \\ -----------------\)
3. \(4x^2+20x=9x^2+9x \\ \Leftrightarrow -5x^2+11x=0 \\ \Leftrightarrow x(-5x+11) = 0 \\ \Leftrightarrow x = 0 \vee -5x+11=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-11}{-5} = \frac{11}{5} \\ V = \Big\{ \frac{11}{5}; 0 \Big\} \\ -----------------\)
4. \(-4x^2-9x=-10x^2-5x \\ \Leftrightarrow 6x^2-4x=0 \\ \Leftrightarrow x(6x-4) = 0 \\ \Leftrightarrow x = 0 \vee 6x-4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{4}{6} = \frac{2}{3} \\ V = \Big\{ \frac{2}{3}; 0 \Big\} \\ -----------------\)
5. \(4(-2x^2+8x)=-(14x^2-29x) \\ \Leftrightarrow -8x^2+32x=-14x^2+29x \\ \Leftrightarrow -8x^2+32x+14x^2-29x= 0 \\ \Leftrightarrow 6x^2-3x=0 \\ \Leftrightarrow x(6x-3) = 0 \\ \Leftrightarrow x = 0 \vee 6x-3=0 \\ \Leftrightarrow x = 0 \vee x = \frac{3}{6} = \frac{1}{2} \\ V = \Big\{ \frac{1}{2}; 0 \Big\} \\ -----------------\)
6. \(-8x^2+8x=0 \\ \Leftrightarrow x(-8x+8) = 0 \\ \Leftrightarrow x = 0 \vee -8x+8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-8}{-8} = 1 \\ V = \Big\{ 1; 0 \Big\} \\ -----------------\)
7. \(-x^2+11x=-6x^2+10x \\ \Leftrightarrow 5x^2+1x=0 \\ \Leftrightarrow x(5x+1) = 0 \\ \Leftrightarrow x = 0 \vee 5x+1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-1}{5} \\ V = \Big\{ 0 ; \frac{-1}{5} \Big\} \\ -----------------\)
8. \(13x^2+27x=8x^2+8x \\ \Leftrightarrow 5x^2+19x=0 \\ \Leftrightarrow x(5x+19) = 0 \\ \Leftrightarrow x = 0 \vee 5x+19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-19}{5} \\ V = \Big\{ 0 ; \frac{-19}{5} \Big\} \\ -----------------\)
9. \(6x^2+9x=0 \\ \Leftrightarrow x(6x+9) = 0 \\ \Leftrightarrow x = 0 \vee 6x+9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-9}{6} = \frac{-3}{2} \\ V = \Big\{ 0 ; \frac{-3}{2} \Big\} \\ -----------------\)
10. \(-4x^2+5x=0 \\ \Leftrightarrow x(-4x+5) = 0 \\ \Leftrightarrow x = 0 \vee -4x+5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-5}{-4} = \frac{5}{4} \\ V = \Big\{ \frac{5}{4}; 0 \Big\} \\ -----------------\)
11. \(-2(-9x^2-7x)=-(-20x^2-2x) \\ \Leftrightarrow 18x^2+14x=20x^2+2x \\ \Leftrightarrow 18x^2+14x-20x^2-2x= 0 \\ \Leftrightarrow -2x^2-12x=0 \\ \Leftrightarrow x(-2x-12) = 0 \\ \Leftrightarrow x = 0 \vee -2x-12=0 \\ \Leftrightarrow x = 0 \vee x = \frac{12}{-2} = -6 \\ V = \Big\{ 0 ; -6 \Big\} \\ -----------------\)
12. \(13x^2-8x=9x^2+7x \\ \Leftrightarrow 4x^2-15x=0 \\ \Leftrightarrow x(4x-15) = 0 \\ \Leftrightarrow x = 0 \vee 4x-15=0 \\ \Leftrightarrow x = 0 \vee x = \frac{15}{4} \\ V = \Big\{ \frac{15}{4}; 0 \Big\} \\ -----------------\)