Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(2(-9x^2-4x)=-(13x^2+32x)\)
2. \(-6x^2+12x=0\)
3. \(3x^2+0x=0\)
4. \(-4(2x^2+4x)=-(16x^2-9x)\)
5. \(-9x^2-11x=-10x^2-6x\)
6. \(-x^2+7x=6x^2-10x\)
7. \(12x^2+16x=5x^2+7x\)
8. \(-3x^2+19x=-6x^2-2x\)
9. \(3(9x^2-4x)=-(-25x^2+13x)\)
10. \(4x^2+10x=0\)
11. \(-5(7x^2+8x)=-(29x^2+58x)\)
12. \(3x^2+25x=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(2(-9x^2-4x)=-(13x^2+32x) \\ \Leftrightarrow -18x^2-8x=-13x^2-32x \\ \Leftrightarrow -18x^2-8x+13x^2+32x= 0 \\ \Leftrightarrow -5x^2-24x=0 \\ \Leftrightarrow x(-5x-24) = 0 \\ \Leftrightarrow x = 0 \vee -5x-24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{24}{-5} = \frac{-24}{5} \\ V = \Big\{ 0 ; \frac{-24}{5} \Big\} \\ -----------------\)
2. \(-6x^2+12x=0 \\ \Leftrightarrow x(-6x+12) = 0 \\ \Leftrightarrow x = 0 \vee -6x+12=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-12}{-6} = 2 \\ V = \Big\{ 2; 0 \Big\} \\ -----------------\)
3. \(3x^2+0x=0 \\ \Leftrightarrow 3x^2=0 \\ \Leftrightarrow x^2 = \frac{0}{3} \\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
4. \(-4(2x^2+4x)=-(16x^2-9x) \\ \Leftrightarrow -8x^2-16x=-16x^2+9x \\ \Leftrightarrow -8x^2-16x+16x^2-9x= 0 \\ \Leftrightarrow 8x^2+25x=0 \\ \Leftrightarrow x(8x+25) = 0 \\ \Leftrightarrow x = 0 \vee 8x+25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-25}{8} \\ V = \Big\{ 0 ; \frac{-25}{8} \Big\} \\ -----------------\)
5. \(-9x^2-11x=-10x^2-6x \\ \Leftrightarrow x^2-5x=0 \\ \Leftrightarrow x(x-5) = 0 \\ \Leftrightarrow x = 0 \vee x-5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{5}{1} = 5 \\ V = \Big\{ 5; 0 \Big\} \\ -----------------\)
6. \(-x^2+7x=6x^2-10x \\ \Leftrightarrow -7x^2+17x=0 \\ \Leftrightarrow x(-7x+17) = 0 \\ \Leftrightarrow x = 0 \vee -7x+17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-17}{-7} = \frac{17}{7} \\ V = \Big\{ \frac{17}{7}; 0 \Big\} \\ -----------------\)
7. \(12x^2+16x=5x^2+7x \\ \Leftrightarrow 7x^2+9x=0 \\ \Leftrightarrow x(7x+9) = 0 \\ \Leftrightarrow x = 0 \vee 7x+9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-9}{7} \\ V = \Big\{ 0 ; \frac{-9}{7} \Big\} \\ -----------------\)
8. \(-3x^2+19x=-6x^2-2x \\ \Leftrightarrow 3x^2+21x=0 \\ \Leftrightarrow x(3x+21) = 0 \\ \Leftrightarrow x = 0 \vee 3x+21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-21}{3} = -7 \\ V = \Big\{ 0 ; -7 \Big\} \\ -----------------\)
9. \(3(9x^2-4x)=-(-25x^2+13x) \\ \Leftrightarrow 27x^2-12x=25x^2-13x \\ \Leftrightarrow 27x^2-12x-25x^2+13x= 0 \\ \Leftrightarrow 2x^2-1x=0 \\ \Leftrightarrow x(2x-1) = 0 \\ \Leftrightarrow x = 0 \vee 2x-1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{1}{2} \\ V = \Big\{ \frac{1}{2}; 0 \Big\} \\ -----------------\)
10. \(4x^2+10x=0 \\ \Leftrightarrow x(4x+10) = 0 \\ \Leftrightarrow x = 0 \vee 4x+10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-10}{4} = \frac{-5}{2} \\ V = \Big\{ 0 ; \frac{-5}{2} \Big\} \\ -----------------\)
11. \(-5(7x^2+8x)=-(29x^2+58x) \\ \Leftrightarrow -35x^2-40x=-29x^2-58x \\ \Leftrightarrow -35x^2-40x+29x^2+58x= 0 \\ \Leftrightarrow -6x^2-18x=0 \\ \Leftrightarrow x(-6x-18) = 0 \\ \Leftrightarrow x = 0 \vee -6x-18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{18}{-6} = -3 \\ V = \Big\{ 0 ; -3 \Big\} \\ -----------------\)
12. \(3x^2+25x=0 \\ \Leftrightarrow x(3x+25) = 0 \\ \Leftrightarrow x = 0 \vee 3x+25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-25}{3} \\ V = \Big\{ 0 ; \frac{-25}{3} \Big\} \\ -----------------\)