Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(4(7x^2+10x)=-(-29x^2-44x)\)
2. \(-13x^2-23x=-5x^2-6x\)
3. \(-5x^2-1x=0\)
4. \(4x^2+20x=7x^2-2x\)
5. \(-x^2-17x=0\)
6. \(-6x^2-30x=-10x^2-10x\)
7. \(8x^2-19x=0\)
8. \(2(-4x^2+6x)=-(6x^2-17x)\)
9. \(-2x^2-3x=0\)
10. \(-2x^2-21x=-6x^2-3x\)
11. \(4x^2+11x=-4x^2+5x\)
12. \(-4(7x^2+4x)=-(22x^2+37x)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(4(7x^2+10x)=-(-29x^2-44x) \\ \Leftrightarrow 28x^2+40x=29x^2+44x \\ \Leftrightarrow 28x^2+40x-29x^2-44x= 0 \\ \Leftrightarrow -x^2+4x=0 \\ \Leftrightarrow x(-x+4) = 0 \\ \Leftrightarrow x = 0 \vee -x+4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-4}{-1} = 4 \\ V = \Big\{ 4; 0 \Big\} \\ -----------------\)
2. \(-13x^2-23x=-5x^2-6x \\ \Leftrightarrow -8x^2-17x=0 \\ \Leftrightarrow x(-8x-17) = 0 \\ \Leftrightarrow x = 0 \vee -8x-17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{17}{-8} = \frac{-17}{8} \\ V = \Big\{ 0 ; \frac{-17}{8} \Big\} \\ -----------------\)
3. \(-5x^2-1x=0 \\ \Leftrightarrow x(-5x-1) = 0 \\ \Leftrightarrow x = 0 \vee -5x-1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{1}{-5} = \frac{-1}{5} \\ V = \Big\{ 0 ; \frac{-1}{5} \Big\} \\ -----------------\)
4. \(4x^2+20x=7x^2-2x \\ \Leftrightarrow -3x^2+22x=0 \\ \Leftrightarrow x(-3x+22) = 0 \\ \Leftrightarrow x = 0 \vee -3x+22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-22}{-3} = \frac{22}{3} \\ V = \Big\{ \frac{22}{3}; 0 \Big\} \\ -----------------\)
5. \(-x^2-17x=0 \\ \Leftrightarrow x(-x-17) = 0 \\ \Leftrightarrow x = 0 \vee -x-17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{17}{-1} = -17 \\ V = \Big\{ 0 ; -17 \Big\} \\ -----------------\)
6. \(-6x^2-30x=-10x^2-10x \\ \Leftrightarrow 4x^2-20x=0 \\ \Leftrightarrow x(4x-20) = 0 \\ \Leftrightarrow x = 0 \vee 4x-20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{20}{4} = 5 \\ V = \Big\{ 5; 0 \Big\} \\ -----------------\)
7. \(8x^2-19x=0 \\ \Leftrightarrow x(8x-19) = 0 \\ \Leftrightarrow x = 0 \vee 8x-19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{19}{8} \\ V = \Big\{ \frac{19}{8}; 0 \Big\} \\ -----------------\)
8. \(2(-4x^2+6x)=-(6x^2-17x) \\ \Leftrightarrow -8x^2+12x=-6x^2+17x \\ \Leftrightarrow -8x^2+12x+6x^2-17x= 0 \\ \Leftrightarrow -2x^2+5x=0 \\ \Leftrightarrow x(-2x+5) = 0 \\ \Leftrightarrow x = 0 \vee -2x+5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-5}{-2} = \frac{5}{2} \\ V = \Big\{ \frac{5}{2}; 0 \Big\} \\ -----------------\)
9. \(-2x^2-3x=0 \\ \Leftrightarrow x(-2x-3) = 0 \\ \Leftrightarrow x = 0 \vee -2x-3=0 \\ \Leftrightarrow x = 0 \vee x = \frac{3}{-2} = \frac{-3}{2} \\ V = \Big\{ 0 ; \frac{-3}{2} \Big\} \\ -----------------\)
10. \(-2x^2-21x=-6x^2-3x \\ \Leftrightarrow 4x^2-18x=0 \\ \Leftrightarrow x(4x-18) = 0 \\ \Leftrightarrow x = 0 \vee 4x-18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{18}{4} = \frac{9}{2} \\ V = \Big\{ \frac{9}{2}; 0 \Big\} \\ -----------------\)
11. \(4x^2+11x=-4x^2+5x \\ \Leftrightarrow 8x^2+6x=0 \\ \Leftrightarrow x(8x+6) = 0 \\ \Leftrightarrow x = 0 \vee 8x+6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-6}{8} = \frac{-3}{4} \\ V = \Big\{ 0 ; \frac{-3}{4} \Big\} \\ -----------------\)
12. \(-4(7x^2+4x)=-(22x^2+37x) \\ \Leftrightarrow -28x^2-16x=-22x^2-37x \\ \Leftrightarrow -28x^2-16x+22x^2+37x= 0 \\ \Leftrightarrow -6x^2-21x=0 \\ \Leftrightarrow x(-6x-21) = 0 \\ \Leftrightarrow x = 0 \vee -6x-21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{21}{-6} = \frac{-7}{2} \\ V = \Big\{ 0 ; \frac{-7}{2} \Big\} \\ -----------------\)