Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-17x^2-4x=-9x^2-8x\)
2. \(9x^2-22x=10x^2-10x\)
3. \(3x^2+6x=9x^2-9x\)
4. \(-2(6x^2-6x)=-(8x^2+13x)\)
5. \(4x^2+12x=8x^2+8x\)
6. \(-5(4x^2+2x)=-(27x^2-9x)\)
7. \(-x^2+22x=0\)
8. \(-5(-5x^2-8x)=-(-33x^2-30x)\)
9. \(-2x^2+13x=0\)
10. \(4x^2+15x=-3x^2+10x\)
11. \(-3x^2-13x=-10x^2-9x\)
12. \(7x^2+2x=3x^2+8x\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-17x^2-4x=-9x^2-8x \\ \Leftrightarrow -8x^2+4x=0 \\ \Leftrightarrow x(-8x+4) = 0 \\ \Leftrightarrow x = 0 \vee -8x+4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-4}{-8} = \frac{1}{2} \\ V = \Big\{ \frac{1}{2}; 0 \Big\} \\ -----------------\)
2. \(9x^2-22x=10x^2-10x \\ \Leftrightarrow -x^2-12x=0 \\ \Leftrightarrow x(-x-12) = 0 \\ \Leftrightarrow x = 0 \vee -x-12=0 \\ \Leftrightarrow x = 0 \vee x = \frac{12}{-1} = -12 \\ V = \Big\{ 0 ; -12 \Big\} \\ -----------------\)
3. \(3x^2+6x=9x^2-9x \\ \Leftrightarrow -6x^2+15x=0 \\ \Leftrightarrow x(-6x+15) = 0 \\ \Leftrightarrow x = 0 \vee -6x+15=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-15}{-6} = \frac{5}{2} \\ V = \Big\{ \frac{5}{2}; 0 \Big\} \\ -----------------\)
4. \(-2(6x^2-6x)=-(8x^2+13x) \\ \Leftrightarrow -12x^2+12x=-8x^2-13x \\ \Leftrightarrow -12x^2+12x+8x^2+13x= 0 \\ \Leftrightarrow -4x^2-25x=0 \\ \Leftrightarrow x(-4x-25) = 0 \\ \Leftrightarrow x = 0 \vee -4x-25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{25}{-4} = \frac{-25}{4} \\ V = \Big\{ 0 ; \frac{-25}{4} \Big\} \\ -----------------\)
5. \(4x^2+12x=8x^2+8x \\ \Leftrightarrow -4x^2+4x=0 \\ \Leftrightarrow x(-4x+4) = 0 \\ \Leftrightarrow x = 0 \vee -4x+4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-4}{-4} = 1 \\ V = \Big\{ 1; 0 \Big\} \\ -----------------\)
6. \(-5(4x^2+2x)=-(27x^2-9x) \\ \Leftrightarrow -20x^2-10x=-27x^2+9x \\ \Leftrightarrow -20x^2-10x+27x^2-9x= 0 \\ \Leftrightarrow 7x^2+19x=0 \\ \Leftrightarrow x(7x+19) = 0 \\ \Leftrightarrow x = 0 \vee 7x+19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-19}{7} \\ V = \Big\{ 0 ; \frac{-19}{7} \Big\} \\ -----------------\)
7. \(-x^2+22x=0 \\ \Leftrightarrow x(-x+22) = 0 \\ \Leftrightarrow x = 0 \vee -x+22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-22}{-1} = 22 \\ V = \Big\{ 22; 0 \Big\} \\ -----------------\)
8. \(-5(-5x^2-8x)=-(-33x^2-30x) \\ \Leftrightarrow 25x^2+40x=33x^2+30x \\ \Leftrightarrow 25x^2+40x-33x^2-30x= 0 \\ \Leftrightarrow -8x^2-10x=0 \\ \Leftrightarrow x(-8x-10) = 0 \\ \Leftrightarrow x = 0 \vee -8x-10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{10}{-8} = \frac{-5}{4} \\ V = \Big\{ 0 ; \frac{-5}{4} \Big\} \\ -----------------\)
9. \(-2x^2+13x=0 \\ \Leftrightarrow x(-2x+13) = 0 \\ \Leftrightarrow x = 0 \vee -2x+13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-13}{-2} = \frac{13}{2} \\ V = \Big\{ \frac{13}{2}; 0 \Big\} \\ -----------------\)
10. \(4x^2+15x=-3x^2+10x \\ \Leftrightarrow 7x^2+5x=0 \\ \Leftrightarrow x(7x+5) = 0 \\ \Leftrightarrow x = 0 \vee 7x+5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-5}{7} \\ V = \Big\{ 0 ; \frac{-5}{7} \Big\} \\ -----------------\)
11. \(-3x^2-13x=-10x^2-9x \\ \Leftrightarrow 7x^2-4x=0 \\ \Leftrightarrow x(7x-4) = 0 \\ \Leftrightarrow x = 0 \vee 7x-4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{4}{7} \\ V = \Big\{ \frac{4}{7}; 0 \Big\} \\ -----------------\)
12. \(7x^2+2x=3x^2+8x \\ \Leftrightarrow 4x^2-6x=0 \\ \Leftrightarrow x(4x-6) = 0 \\ \Leftrightarrow x = 0 \vee 4x-6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{6}{4} = \frac{3}{2} \\ V = \Big\{ \frac{3}{2}; 0 \Big\} \\ -----------------\)