Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-x^2-20x=0\)
2. \(2(-9x^2+9x)=-(14x^2+6x)\)
3. \(-2(6x^2+8x)=-(9x^2+11x)\)
4. \(-3x^2-13x=-7x^2+2x\)
5. \(5x^2-15x=-2x^2-10x\)
6. \(4(7x^2-4x)=-(-36x^2+24x)\)
7. \(4x^2-29x=7x^2-7x\)
8. \(8x^2-12x=0\)
9. \(-4(-10x^2-5x)=-(-45x^2-29x)\)
10. \(-7x^2-20x=0\)
11. \(5x^2-8x=0\)
12. \(-4x^2-8x=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-x^2-20x=0 \\ \Leftrightarrow x(-x-20) = 0 \\ \Leftrightarrow x = 0 \vee -x-20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{20}{-1} = -20 \\ V = \Big\{ 0 ; -20 \Big\} \\ -----------------\)
2. \(2(-9x^2+9x)=-(14x^2+6x) \\ \Leftrightarrow -18x^2+18x=-14x^2-6x \\ \Leftrightarrow -18x^2+18x+14x^2+6x= 0 \\ \Leftrightarrow -4x^2-24x=0 \\ \Leftrightarrow x(-4x-24) = 0 \\ \Leftrightarrow x = 0 \vee -4x-24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{24}{-4} = -6 \\ V = \Big\{ 0 ; -6 \Big\} \\ -----------------\)
3. \(-2(6x^2+8x)=-(9x^2+11x) \\ \Leftrightarrow -12x^2-16x=-9x^2-11x \\ \Leftrightarrow -12x^2-16x+9x^2+11x= 0 \\ \Leftrightarrow -3x^2+5x=0 \\ \Leftrightarrow x(-3x+5) = 0 \\ \Leftrightarrow x = 0 \vee -3x+5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-5}{-3} = \frac{5}{3} \\ V = \Big\{ \frac{5}{3}; 0 \Big\} \\ -----------------\)
4. \(-3x^2-13x=-7x^2+2x \\ \Leftrightarrow 4x^2-15x=0 \\ \Leftrightarrow x(4x-15) = 0 \\ \Leftrightarrow x = 0 \vee 4x-15=0 \\ \Leftrightarrow x = 0 \vee x = \frac{15}{4} \\ V = \Big\{ \frac{15}{4}; 0 \Big\} \\ -----------------\)
5. \(5x^2-15x=-2x^2-10x \\ \Leftrightarrow 7x^2-5x=0 \\ \Leftrightarrow x(7x-5) = 0 \\ \Leftrightarrow x = 0 \vee 7x-5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{5}{7} \\ V = \Big\{ \frac{5}{7}; 0 \Big\} \\ -----------------\)
6. \(4(7x^2-4x)=-(-36x^2+24x) \\ \Leftrightarrow 28x^2-16x=36x^2-24x \\ \Leftrightarrow 28x^2-16x-36x^2+24x= 0 \\ \Leftrightarrow -8x^2-8x=0 \\ \Leftrightarrow x(-8x-8) = 0 \\ \Leftrightarrow x = 0 \vee -8x-8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{8}{-8} = -1 \\ V = \Big\{ 0 ; -1 \Big\} \\ -----------------\)
7. \(4x^2-29x=7x^2-7x \\ \Leftrightarrow -3x^2-22x=0 \\ \Leftrightarrow x(-3x-22) = 0 \\ \Leftrightarrow x = 0 \vee -3x-22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{22}{-3} = \frac{-22}{3} \\ V = \Big\{ 0 ; \frac{-22}{3} \Big\} \\ -----------------\)
8. \(8x^2-12x=0 \\ \Leftrightarrow x(8x-12) = 0 \\ \Leftrightarrow x = 0 \vee 8x-12=0 \\ \Leftrightarrow x = 0 \vee x = \frac{12}{8} = \frac{3}{2} \\ V = \Big\{ \frac{3}{2}; 0 \Big\} \\ -----------------\)
9. \(-4(-10x^2-5x)=-(-45x^2-29x) \\ \Leftrightarrow 40x^2+20x=45x^2+29x \\ \Leftrightarrow 40x^2+20x-45x^2-29x= 0 \\ \Leftrightarrow -5x^2+9x=0 \\ \Leftrightarrow x(-5x+9) = 0 \\ \Leftrightarrow x = 0 \vee -5x+9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-9}{-5} = \frac{9}{5} \\ V = \Big\{ \frac{9}{5}; 0 \Big\} \\ -----------------\)
10. \(-7x^2-20x=0 \\ \Leftrightarrow x(-7x-20) = 0 \\ \Leftrightarrow x = 0 \vee -7x-20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{20}{-7} = \frac{-20}{7} \\ V = \Big\{ 0 ; \frac{-20}{7} \Big\} \\ -----------------\)
11. \(5x^2-8x=0 \\ \Leftrightarrow x(5x-8) = 0 \\ \Leftrightarrow x = 0 \vee 5x-8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{8}{5} \\ V = \Big\{ \frac{8}{5}; 0 \Big\} \\ -----------------\)
12. \(-4x^2-8x=0 \\ \Leftrightarrow x(-4x-8) = 0 \\ \Leftrightarrow x = 0 \vee -4x-8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{8}{-4} = -2 \\ V = \Big\{ 0 ; -2 \Big\} \\ -----------------\)