Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(7x^2+17x=0\)
2. \(5x^2-5x=0\)
3. \(16x^2-3x=9x^2-6x\)
4. \(-x^2-13x=7x^2+3x\)
5. \(-10x^2-x=-2x^2+3x\)
6. \(5(-9x^2-9x)=-(49x^2+45x)\)
7. \(3(3x^2-8x)=-(-13x^2+2x)\)
8. \(-x^2+6x=0\)
9. \(x^2-25x=0\)
10. \(4x^2-11x=0\)
11. \(-5(6x^2+3x)=-(32x^2+23x)\)
12. \(-7x^2+15x=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(7x^2+17x=0 \\ \Leftrightarrow x(7x+17) = 0 \\ \Leftrightarrow x = 0 \vee 7x+17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-17}{7} \\ V = \Big\{ 0 ; \frac{-17}{7} \Big\} \\ -----------------\)
2. \(5x^2-5x=0 \\ \Leftrightarrow x(5x-5) = 0 \\ \Leftrightarrow x = 0 \vee 5x-5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{5}{5} = 1 \\ V = \Big\{ 1; 0 \Big\} \\ -----------------\)
3. \(16x^2-3x=9x^2-6x \\ \Leftrightarrow 7x^2+3x=0 \\ \Leftrightarrow x(7x+3) = 0 \\ \Leftrightarrow x = 0 \vee 7x+3=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-3}{7} \\ V = \Big\{ 0 ; \frac{-3}{7} \Big\} \\ -----------------\)
4. \(-x^2-13x=7x^2+3x \\ \Leftrightarrow -8x^2-16x=0 \\ \Leftrightarrow x(-8x-16) = 0 \\ \Leftrightarrow x = 0 \vee -8x-16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{16}{-8} = -2 \\ V = \Big\{ 0 ; -2 \Big\} \\ -----------------\)
5. \(-10x^2-x=-2x^2+3x \\ \Leftrightarrow -8x^2-4x=0 \\ \Leftrightarrow x(-8x-4) = 0 \\ \Leftrightarrow x = 0 \vee -8x-4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{4}{-8} = \frac{-1}{2} \\ V = \Big\{ 0 ; \frac{-1}{2} \Big\} \\ -----------------\)
6. \(5(-9x^2-9x)=-(49x^2+45x) \\ \Leftrightarrow -45x^2-45x=-49x^2-45x \\ \Leftrightarrow -45x^2-45x+49x^2+45x= 0 \\ \Leftrightarrow 4x^2+0x=0 \\ \Leftrightarrow 4x^2=0 \\ \Leftrightarrow x^2 = \frac{0}{4} \\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
7. \(3(3x^2-8x)=-(-13x^2+2x) \\ \Leftrightarrow 9x^2-24x=13x^2-2x \\ \Leftrightarrow 9x^2-24x-13x^2+2x= 0 \\ \Leftrightarrow -4x^2+22x=0 \\ \Leftrightarrow x(-4x+22) = 0 \\ \Leftrightarrow x = 0 \vee -4x+22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-22}{-4} = \frac{11}{2} \\ V = \Big\{ \frac{11}{2}; 0 \Big\} \\ -----------------\)
8. \(-x^2+6x=0 \\ \Leftrightarrow x(-x+6) = 0 \\ \Leftrightarrow x = 0 \vee -x+6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-6}{-1} = 6 \\ V = \Big\{ 6; 0 \Big\} \\ -----------------\)
9. \(x^2-25x=0 \\ \Leftrightarrow x(x-25) = 0 \\ \Leftrightarrow x = 0 \vee x-25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{25}{1} = 25 \\ V = \Big\{ 25; 0 \Big\} \\ -----------------\)
10. \(4x^2-11x=0 \\ \Leftrightarrow x(4x-11) = 0 \\ \Leftrightarrow x = 0 \vee 4x-11=0 \\ \Leftrightarrow x = 0 \vee x = \frac{11}{4} \\ V = \Big\{ \frac{11}{4}; 0 \Big\} \\ -----------------\)
11. \(-5(6x^2+3x)=-(32x^2+23x) \\ \Leftrightarrow -30x^2-15x=-32x^2-23x \\ \Leftrightarrow -30x^2-15x+32x^2+23x= 0 \\ \Leftrightarrow 2x^2-8x=0 \\ \Leftrightarrow x(2x-8) = 0 \\ \Leftrightarrow x = 0 \vee 2x-8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{8}{2} = 4 \\ V = \Big\{ 4; 0 \Big\} \\ -----------------\)
12. \(-7x^2+15x=0 \\ \Leftrightarrow x(-7x+15) = 0 \\ \Leftrightarrow x = 0 \vee -7x+15=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-15}{-7} = \frac{15}{7} \\ V = \Big\{ \frac{15}{7}; 0 \Big\} \\ -----------------\)