Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-5x^2+9x=-6x^2-8x\)
2. \(12x^2+12x=9x^2+10x\)
3. \(2x^2-13x=5x^2-10x\)
4. \(4(-4x^2-6x)=-(8x^2+45x)\)
5. \(-x^2+14x=4x^2+8x\)
6. \(-10x^2-4x=-7x^2-4x\)
7. \(-11x^2-x=-5x^2+9x\)
8. \(9x^2+13x=3x^2+8x\)
9. \(5(8x^2-2x)=-(-46x^2-4x)\)
10. \(-6x^2+5x=0\)
11. \(2(8x^2+10x)=-(-18x^2-3x)\)
12. \(7x^2+3x=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-5x^2+9x=-6x^2-8x \\ \Leftrightarrow x^2+17x=0 \\ \Leftrightarrow x(x+17) = 0 \\ \Leftrightarrow x = 0 \vee x+17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-17}{1} = -17 \\ V = \Big\{ 0 ; -17 \Big\} \\ -----------------\)
2. \(12x^2+12x=9x^2+10x \\ \Leftrightarrow 3x^2+2x=0 \\ \Leftrightarrow x(3x+2) = 0 \\ \Leftrightarrow x = 0 \vee 3x+2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-2}{3} \\ V = \Big\{ 0 ; \frac{-2}{3} \Big\} \\ -----------------\)
3. \(2x^2-13x=5x^2-10x \\ \Leftrightarrow -3x^2-3x=0 \\ \Leftrightarrow x(-3x-3) = 0 \\ \Leftrightarrow x = 0 \vee -3x-3=0 \\ \Leftrightarrow x = 0 \vee x = \frac{3}{-3} = -1 \\ V = \Big\{ 0 ; -1 \Big\} \\ -----------------\)
4. \(4(-4x^2-6x)=-(8x^2+45x) \\ \Leftrightarrow -16x^2-24x=-8x^2-45x \\ \Leftrightarrow -16x^2-24x+8x^2+45x= 0 \\ \Leftrightarrow -8x^2-21x=0 \\ \Leftrightarrow x(-8x-21) = 0 \\ \Leftrightarrow x = 0 \vee -8x-21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{21}{-8} = \frac{-21}{8} \\ V = \Big\{ 0 ; \frac{-21}{8} \Big\} \\ -----------------\)
5. \(-x^2+14x=4x^2+8x \\ \Leftrightarrow -5x^2+6x=0 \\ \Leftrightarrow x(-5x+6) = 0 \\ \Leftrightarrow x = 0 \vee -5x+6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-6}{-5} = \frac{6}{5} \\ V = \Big\{ \frac{6}{5}; 0 \Big\} \\ -----------------\)
6. \(-10x^2-4x=-7x^2-4x \\ \Leftrightarrow -3x^2+0x=0 \\ \Leftrightarrow -3x^2=0 \\ \Leftrightarrow x^2 = \frac{0}{-3} \\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
7. \(-11x^2-x=-5x^2+9x \\ \Leftrightarrow -6x^2-10x=0 \\ \Leftrightarrow x(-6x-10) = 0 \\ \Leftrightarrow x = 0 \vee -6x-10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{10}{-6} = \frac{-5}{3} \\ V = \Big\{ 0 ; \frac{-5}{3} \Big\} \\ -----------------\)
8. \(9x^2+13x=3x^2+8x \\ \Leftrightarrow 6x^2+5x=0 \\ \Leftrightarrow x(6x+5) = 0 \\ \Leftrightarrow x = 0 \vee 6x+5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-5}{6} \\ V = \Big\{ 0 ; \frac{-5}{6} \Big\} \\ -----------------\)
9. \(5(8x^2-2x)=-(-46x^2-4x) \\ \Leftrightarrow 40x^2-10x=46x^2+4x \\ \Leftrightarrow 40x^2-10x-46x^2-4x= 0 \\ \Leftrightarrow -6x^2+14x=0 \\ \Leftrightarrow x(-6x+14) = 0 \\ \Leftrightarrow x = 0 \vee -6x+14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-14}{-6} = \frac{7}{3} \\ V = \Big\{ \frac{7}{3}; 0 \Big\} \\ -----------------\)
10. \(-6x^2+5x=0 \\ \Leftrightarrow x(-6x+5) = 0 \\ \Leftrightarrow x = 0 \vee -6x+5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-5}{-6} = \frac{5}{6} \\ V = \Big\{ \frac{5}{6}; 0 \Big\} \\ -----------------\)
11. \(2(8x^2+10x)=-(-18x^2-3x) \\ \Leftrightarrow 16x^2+20x=18x^2+3x \\ \Leftrightarrow 16x^2+20x-18x^2-3x= 0 \\ \Leftrightarrow -2x^2-17x=0 \\ \Leftrightarrow x(-2x-17) = 0 \\ \Leftrightarrow x = 0 \vee -2x-17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{17}{-2} = \frac{-17}{2} \\ V = \Big\{ 0 ; \frac{-17}{2} \Big\} \\ -----------------\)
12. \(7x^2+3x=0 \\ \Leftrightarrow x(7x+3) = 0 \\ \Leftrightarrow x = 0 \vee 7x+3=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-3}{7} \\ V = \Big\{ 0 ; \frac{-3}{7} \Big\} \\ -----------------\)