Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(13x^2+7x=8x^2-7x\)
2. \(-x^2+13x=0\)
3. \(15x^2+12x=7x^2-4x\)
4. \(-2(-4x^2+7x)=-(-2x^2+25x)\)
5. \(-4(-10x^2+4x)=-(-45x^2-4x)\)
6. \(-3x^2+20x=-4x^2+7x\)
7. \(9x^2-15x=7x^2-10x\)
8. \(5(8x^2-10x)=-(-44x^2+47x)\)
9. \(-7x^2-15x=-8x^2-4x\)
10. \(-3x^2-4x=-10x^2+3x\)
11. \(3(2x^2+5x)=-(-9x^2-26x)\)
12. \(2x^2+11x=8x^2+6x\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(13x^2+7x=8x^2-7x \\ \Leftrightarrow 5x^2+14x=0 \\ \Leftrightarrow x(5x+14) = 0 \\ \Leftrightarrow x = 0 \vee 5x+14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-14}{5} \\ V = \Big\{ 0 ; \frac{-14}{5} \Big\} \\ -----------------\)
2. \(-x^2+13x=0 \\ \Leftrightarrow x(-x+13) = 0 \\ \Leftrightarrow x = 0 \vee -x+13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-13}{-1} = 13 \\ V = \Big\{ 13; 0 \Big\} \\ -----------------\)
3. \(15x^2+12x=7x^2-4x \\ \Leftrightarrow 8x^2+16x=0 \\ \Leftrightarrow x(8x+16) = 0 \\ \Leftrightarrow x = 0 \vee 8x+16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-16}{8} = -2 \\ V = \Big\{ 0 ; -2 \Big\} \\ -----------------\)
4. \(-2(-4x^2+7x)=-(-2x^2+25x) \\ \Leftrightarrow 8x^2-14x=2x^2-25x \\ \Leftrightarrow 8x^2-14x-2x^2+25x= 0 \\ \Leftrightarrow 6x^2-11x=0 \\ \Leftrightarrow x(6x-11) = 0 \\ \Leftrightarrow x = 0 \vee 6x-11=0 \\ \Leftrightarrow x = 0 \vee x = \frac{11}{6} \\ V = \Big\{ \frac{11}{6}; 0 \Big\} \\ -----------------\)
5. \(-4(-10x^2+4x)=-(-45x^2-4x) \\ \Leftrightarrow 40x^2-16x=45x^2+4x \\ \Leftrightarrow 40x^2-16x-45x^2-4x= 0 \\ \Leftrightarrow -5x^2+20x=0 \\ \Leftrightarrow x(-5x+20) = 0 \\ \Leftrightarrow x = 0 \vee -5x+20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-20}{-5} = 4 \\ V = \Big\{ 4; 0 \Big\} \\ -----------------\)
6. \(-3x^2+20x=-4x^2+7x \\ \Leftrightarrow x^2+13x=0 \\ \Leftrightarrow x(x+13) = 0 \\ \Leftrightarrow x = 0 \vee x+13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-13}{1} = -13 \\ V = \Big\{ 0 ; -13 \Big\} \\ -----------------\)
7. \(9x^2-15x=7x^2-10x \\ \Leftrightarrow 2x^2-5x=0 \\ \Leftrightarrow x(2x-5) = 0 \\ \Leftrightarrow x = 0 \vee 2x-5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{5}{2} \\ V = \Big\{ \frac{5}{2}; 0 \Big\} \\ -----------------\)
8. \(5(8x^2-10x)=-(-44x^2+47x) \\ \Leftrightarrow 40x^2-50x=44x^2-47x \\ \Leftrightarrow 40x^2-50x-44x^2+47x= 0 \\ \Leftrightarrow -4x^2+3x=0 \\ \Leftrightarrow x(-4x+3) = 0 \\ \Leftrightarrow x = 0 \vee -4x+3=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-3}{-4} = \frac{3}{4} \\ V = \Big\{ \frac{3}{4}; 0 \Big\} \\ -----------------\)
9. \(-7x^2-15x=-8x^2-4x \\ \Leftrightarrow x^2-11x=0 \\ \Leftrightarrow x(x-11) = 0 \\ \Leftrightarrow x = 0 \vee x-11=0 \\ \Leftrightarrow x = 0 \vee x = \frac{11}{1} = 11 \\ V = \Big\{ 11; 0 \Big\} \\ -----------------\)
10. \(-3x^2-4x=-10x^2+3x \\ \Leftrightarrow 7x^2-7x=0 \\ \Leftrightarrow x(7x-7) = 0 \\ \Leftrightarrow x = 0 \vee 7x-7=0 \\ \Leftrightarrow x = 0 \vee x = \frac{7}{7} = 1 \\ V = \Big\{ 1; 0 \Big\} \\ -----------------\)
11. \(3(2x^2+5x)=-(-9x^2-26x) \\ \Leftrightarrow 6x^2+15x=9x^2+26x \\ \Leftrightarrow 6x^2+15x-9x^2-26x= 0 \\ \Leftrightarrow -3x^2+11x=0 \\ \Leftrightarrow x(-3x+11) = 0 \\ \Leftrightarrow x = 0 \vee -3x+11=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-11}{-3} = \frac{11}{3} \\ V = \Big\{ \frac{11}{3}; 0 \Big\} \\ -----------------\)
12. \(2x^2+11x=8x^2+6x \\ \Leftrightarrow -6x^2+5x=0 \\ \Leftrightarrow x(-6x+5) = 0 \\ \Leftrightarrow x = 0 \vee -6x+5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-5}{-6} = \frac{5}{6} \\ V = \Big\{ \frac{5}{6}; 0 \Big\} \\ -----------------\)