Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-7x^2-13x=-8x^2+7x\)
2. \(-5x^2+6x=0\)
3. \(-2x^2+10x=0\)
4. \(5x^2+19x=0\)
5. \(-4(10x^2+10x)=-(48x^2+28x)\)
6. \(-9x^2+8x=-4x^2+5x\)
7. \(3x^2-22x=0\)
8. \(-2x^2+9x=0\)
9. \(-3(3x^2-10x)=-(4x^2-28x)\)
10. \(2(9x^2+5x)=-(-14x^2-29x)\)
11. \(-x^2+13x=0\)
12. \(-3(3x^2+2x)=-(13x^2+27x)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-7x^2-13x=-8x^2+7x \\ \Leftrightarrow x^2-20x=0 \\ \Leftrightarrow x(x-20) = 0 \\ \Leftrightarrow x = 0 \vee x-20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{20}{1} = 20 \\ V = \Big\{ 20; 0 \Big\} \\ -----------------\)
2. \(-5x^2+6x=0 \\ \Leftrightarrow x(-5x+6) = 0 \\ \Leftrightarrow x = 0 \vee -5x+6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-6}{-5} = \frac{6}{5} \\ V = \Big\{ \frac{6}{5}; 0 \Big\} \\ -----------------\)
3. \(-2x^2+10x=0 \\ \Leftrightarrow x(-2x+10) = 0 \\ \Leftrightarrow x = 0 \vee -2x+10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-10}{-2} = 5 \\ V = \Big\{ 5; 0 \Big\} \\ -----------------\)
4. \(5x^2+19x=0 \\ \Leftrightarrow x(5x+19) = 0 \\ \Leftrightarrow x = 0 \vee 5x+19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-19}{5} \\ V = \Big\{ 0 ; \frac{-19}{5} \Big\} \\ -----------------\)
5. \(-4(10x^2+10x)=-(48x^2+28x) \\ \Leftrightarrow -40x^2-40x=-48x^2-28x \\ \Leftrightarrow -40x^2-40x+48x^2+28x= 0 \\ \Leftrightarrow 8x^2+12x=0 \\ \Leftrightarrow x(8x+12) = 0 \\ \Leftrightarrow x = 0 \vee 8x+12=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-12}{8} = \frac{-3}{2} \\ V = \Big\{ 0 ; \frac{-3}{2} \Big\} \\ -----------------\)
6. \(-9x^2+8x=-4x^2+5x \\ \Leftrightarrow -5x^2+3x=0 \\ \Leftrightarrow x(-5x+3) = 0 \\ \Leftrightarrow x = 0 \vee -5x+3=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-3}{-5} = \frac{3}{5} \\ V = \Big\{ \frac{3}{5}; 0 \Big\} \\ -----------------\)
7. \(3x^2-22x=0 \\ \Leftrightarrow x(3x-22) = 0 \\ \Leftrightarrow x = 0 \vee 3x-22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{22}{3} \\ V = \Big\{ \frac{22}{3}; 0 \Big\} \\ -----------------\)
8. \(-2x^2+9x=0 \\ \Leftrightarrow x(-2x+9) = 0 \\ \Leftrightarrow x = 0 \vee -2x+9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-9}{-2} = \frac{9}{2} \\ V = \Big\{ \frac{9}{2}; 0 \Big\} \\ -----------------\)
9. \(-3(3x^2-10x)=-(4x^2-28x) \\ \Leftrightarrow -9x^2+30x=-4x^2+28x \\ \Leftrightarrow -9x^2+30x+4x^2-28x= 0 \\ \Leftrightarrow -5x^2-2x=0 \\ \Leftrightarrow x(-5x-2) = 0 \\ \Leftrightarrow x = 0 \vee -5x-2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{2}{-5} = \frac{-2}{5} \\ V = \Big\{ 0 ; \frac{-2}{5} \Big\} \\ -----------------\)
10. \(2(9x^2+5x)=-(-14x^2-29x) \\ \Leftrightarrow 18x^2+10x=14x^2+29x \\ \Leftrightarrow 18x^2+10x-14x^2-29x= 0 \\ \Leftrightarrow 4x^2+19x=0 \\ \Leftrightarrow x(4x+19) = 0 \\ \Leftrightarrow x = 0 \vee 4x+19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-19}{4} \\ V = \Big\{ 0 ; \frac{-19}{4} \Big\} \\ -----------------\)
11. \(-x^2+13x=0 \\ \Leftrightarrow x(-x+13) = 0 \\ \Leftrightarrow x = 0 \vee -x+13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-13}{-1} = 13 \\ V = \Big\{ 13; 0 \Big\} \\ -----------------\)
12. \(-3(3x^2+2x)=-(13x^2+27x) \\ \Leftrightarrow -9x^2-6x=-13x^2-27x \\ \Leftrightarrow -9x^2-6x+13x^2+27x= 0 \\ \Leftrightarrow 4x^2-21x=0 \\ \Leftrightarrow x(4x-21) = 0 \\ \Leftrightarrow x = 0 \vee 4x-21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{21}{4} \\ V = \Big\{ \frac{21}{4}; 0 \Big\} \\ -----------------\)