Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-14x^2+34x=-10x^2+10x\)
2. \(x^2+13x=0\)
3. \(3x^2+2x=0\)
4. \(-3(-7x^2+10x)=-(-24x^2+24x)\)
5. \(2x^2-15x=0\)
6. \(-3(-3x^2+3x)=-(-13x^2+31x)\)
7. \(-x^2-12x=3x^2+9x\)
8. \(12x^2+2x=8x^2+5x\)
9. \(-4(7x^2+6x)=-(20x^2+39x)\)
10. \(9x^2+16x=10x^2-6x\)
11. \(-4(3x^2+8x)=-(17x^2+26x)\)
12. \(8x^2-22x=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-14x^2+34x=-10x^2+10x \\ \Leftrightarrow -4x^2+24x=0 \\ \Leftrightarrow x(-4x+24) = 0 \\ \Leftrightarrow x = 0 \vee -4x+24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-24}{-4} = 6 \\ V = \Big\{ 6; 0 \Big\} \\ -----------------\)
2. \(x^2+13x=0 \\ \Leftrightarrow x(x+13) = 0 \\ \Leftrightarrow x = 0 \vee x+13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-13}{1} = -13 \\ V = \Big\{ 0 ; -13 \Big\} \\ -----------------\)
3. \(3x^2+2x=0 \\ \Leftrightarrow x(3x+2) = 0 \\ \Leftrightarrow x = 0 \vee 3x+2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-2}{3} \\ V = \Big\{ 0 ; \frac{-2}{3} \Big\} \\ -----------------\)
4. \(-3(-7x^2+10x)=-(-24x^2+24x) \\ \Leftrightarrow 21x^2-30x=24x^2-24x \\ \Leftrightarrow 21x^2-30x-24x^2+24x= 0 \\ \Leftrightarrow -3x^2+6x=0 \\ \Leftrightarrow x(-3x+6) = 0 \\ \Leftrightarrow x = 0 \vee -3x+6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-6}{-3} = 2 \\ V = \Big\{ 2; 0 \Big\} \\ -----------------\)
5. \(2x^2-15x=0 \\ \Leftrightarrow x(2x-15) = 0 \\ \Leftrightarrow x = 0 \vee 2x-15=0 \\ \Leftrightarrow x = 0 \vee x = \frac{15}{2} \\ V = \Big\{ \frac{15}{2}; 0 \Big\} \\ -----------------\)
6. \(-3(-3x^2+3x)=-(-13x^2+31x) \\ \Leftrightarrow 9x^2-9x=13x^2-31x \\ \Leftrightarrow 9x^2-9x-13x^2+31x= 0 \\ \Leftrightarrow -4x^2-22x=0 \\ \Leftrightarrow x(-4x-22) = 0 \\ \Leftrightarrow x = 0 \vee -4x-22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{22}{-4} = \frac{-11}{2} \\ V = \Big\{ 0 ; \frac{-11}{2} \Big\} \\ -----------------\)
7. \(-x^2-12x=3x^2+9x \\ \Leftrightarrow -4x^2-21x=0 \\ \Leftrightarrow x(-4x-21) = 0 \\ \Leftrightarrow x = 0 \vee -4x-21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{21}{-4} = \frac{-21}{4} \\ V = \Big\{ 0 ; \frac{-21}{4} \Big\} \\ -----------------\)
8. \(12x^2+2x=8x^2+5x \\ \Leftrightarrow 4x^2-3x=0 \\ \Leftrightarrow x(4x-3) = 0 \\ \Leftrightarrow x = 0 \vee 4x-3=0 \\ \Leftrightarrow x = 0 \vee x = \frac{3}{4} \\ V = \Big\{ \frac{3}{4}; 0 \Big\} \\ -----------------\)
9. \(-4(7x^2+6x)=-(20x^2+39x) \\ \Leftrightarrow -28x^2-24x=-20x^2-39x \\ \Leftrightarrow -28x^2-24x+20x^2+39x= 0 \\ \Leftrightarrow -8x^2-15x=0 \\ \Leftrightarrow x(-8x-15) = 0 \\ \Leftrightarrow x = 0 \vee -8x-15=0 \\ \Leftrightarrow x = 0 \vee x = \frac{15}{-8} = \frac{-15}{8} \\ V = \Big\{ 0 ; \frac{-15}{8} \Big\} \\ -----------------\)
10. \(9x^2+16x=10x^2-6x \\ \Leftrightarrow -x^2+22x=0 \\ \Leftrightarrow x(-x+22) = 0 \\ \Leftrightarrow x = 0 \vee -x+22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-22}{-1} = 22 \\ V = \Big\{ 22; 0 \Big\} \\ -----------------\)
11. \(-4(3x^2+8x)=-(17x^2+26x) \\ \Leftrightarrow -12x^2-32x=-17x^2-26x \\ \Leftrightarrow -12x^2-32x+17x^2+26x= 0 \\ \Leftrightarrow 5x^2+6x=0 \\ \Leftrightarrow x(5x+6) = 0 \\ \Leftrightarrow x = 0 \vee 5x+6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-6}{5} \\ V = \Big\{ 0 ; \frac{-6}{5} \Big\} \\ -----------------\)
12. \(8x^2-22x=0 \\ \Leftrightarrow x(8x-22) = 0 \\ \Leftrightarrow x = 0 \vee 8x-22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{22}{8} = \frac{11}{4} \\ V = \Big\{ \frac{11}{4}; 0 \Big\} \\ -----------------\)