Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-5(-6x^2+6x)=-(-34x^2+27x)\)
2. \(-4(-3x^2+9x)=-(-5x^2+15x)\)
3. \(-2(5x^2-2x)=-(12x^2-26x)\)
4. \(-2(4x^2-5x)=-(2x^2-33x)\)
5. \(-2(-5x^2+4x)=-(-14x^2+16x)\)
6. \(4(8x^2-9x)=-(-36x^2+61x)\)
7. \(14x^2+6x=9x^2+7x\)
8. \(-5(-2x^2-2x)=-(-11x^2-29x)\)
9. \(-5(10x^2+3x)=-(53x^2+11x)\)
10. \(5x^2-17x=-3x^2+8x\)
11. \(2x^2-17x=8x^2-5x\)
12. \(5x^2+5x=10x^2-9x\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-5(-6x^2+6x)=-(-34x^2+27x) \\ \Leftrightarrow 30x^2-30x=34x^2-27x \\ \Leftrightarrow 30x^2-30x-34x^2+27x= 0 \\ \Leftrightarrow -4x^2+3x=0 \\ \Leftrightarrow x(-4x+3) = 0 \\ \Leftrightarrow x = 0 \vee -4x+3=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-3}{-4} = \frac{3}{4} \\ V = \Big\{ \frac{3}{4}; 0 \Big\} \\ -----------------\)
2. \(-4(-3x^2+9x)=-(-5x^2+15x) \\ \Leftrightarrow 12x^2-36x=5x^2-15x \\ \Leftrightarrow 12x^2-36x-5x^2+15x= 0 \\ \Leftrightarrow 7x^2+21x=0 \\ \Leftrightarrow x(7x+21) = 0 \\ \Leftrightarrow x = 0 \vee 7x+21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-21}{7} = -3 \\ V = \Big\{ 0 ; -3 \Big\} \\ -----------------\)
3. \(-2(5x^2-2x)=-(12x^2-26x) \\ \Leftrightarrow -10x^2+4x=-12x^2+26x \\ \Leftrightarrow -10x^2+4x+12x^2-26x= 0 \\ \Leftrightarrow 2x^2+22x=0 \\ \Leftrightarrow x(2x+22) = 0 \\ \Leftrightarrow x = 0 \vee 2x+22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-22}{2} = -11 \\ V = \Big\{ 0 ; -11 \Big\} \\ -----------------\)
4. \(-2(4x^2-5x)=-(2x^2-33x) \\ \Leftrightarrow -8x^2+10x=-2x^2+33x \\ \Leftrightarrow -8x^2+10x+2x^2-33x= 0 \\ \Leftrightarrow -6x^2+23x=0 \\ \Leftrightarrow x(-6x+23) = 0 \\ \Leftrightarrow x = 0 \vee -6x+23=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-23}{-6} = \frac{23}{6} \\ V = \Big\{ \frac{23}{6}; 0 \Big\} \\ -----------------\)
5. \(-2(-5x^2+4x)=-(-14x^2+16x) \\ \Leftrightarrow 10x^2-8x=14x^2-16x \\ \Leftrightarrow 10x^2-8x-14x^2+16x= 0 \\ \Leftrightarrow -4x^2-8x=0 \\ \Leftrightarrow x(-4x-8) = 0 \\ \Leftrightarrow x = 0 \vee -4x-8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{8}{-4} = -2 \\ V = \Big\{ 0 ; -2 \Big\} \\ -----------------\)
6. \(4(8x^2-9x)=-(-36x^2+61x) \\ \Leftrightarrow 32x^2-36x=36x^2-61x \\ \Leftrightarrow 32x^2-36x-36x^2+61x= 0 \\ \Leftrightarrow -4x^2-25x=0 \\ \Leftrightarrow x(-4x-25) = 0 \\ \Leftrightarrow x = 0 \vee -4x-25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{25}{-4} = \frac{-25}{4} \\ V = \Big\{ 0 ; \frac{-25}{4} \Big\} \\ -----------------\)
7. \(14x^2+6x=9x^2+7x \\ \Leftrightarrow 5x^2-1x=0 \\ \Leftrightarrow x(5x-1) = 0 \\ \Leftrightarrow x = 0 \vee 5x-1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{1}{5} \\ V = \Big\{ \frac{1}{5}; 0 \Big\} \\ -----------------\)
8. \(-5(-2x^2-2x)=-(-11x^2-29x) \\ \Leftrightarrow 10x^2+10x=11x^2+29x \\ \Leftrightarrow 10x^2+10x-11x^2-29x= 0 \\ \Leftrightarrow -x^2+19x=0 \\ \Leftrightarrow x(-x+19) = 0 \\ \Leftrightarrow x = 0 \vee -x+19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-19}{-1} = 19 \\ V = \Big\{ 19; 0 \Big\} \\ -----------------\)
9. \(-5(10x^2+3x)=-(53x^2+11x) \\ \Leftrightarrow -50x^2-15x=-53x^2-11x \\ \Leftrightarrow -50x^2-15x+53x^2+11x= 0 \\ \Leftrightarrow 3x^2+4x=0 \\ \Leftrightarrow x(3x+4) = 0 \\ \Leftrightarrow x = 0 \vee 3x+4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-4}{3} \\ V = \Big\{ 0 ; \frac{-4}{3} \Big\} \\ -----------------\)
10. \(5x^2-17x=-3x^2+8x \\ \Leftrightarrow 8x^2-25x=0 \\ \Leftrightarrow x(8x-25) = 0 \\ \Leftrightarrow x = 0 \vee 8x-25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{25}{8} \\ V = \Big\{ \frac{25}{8}; 0 \Big\} \\ -----------------\)
11. \(2x^2-17x=8x^2-5x \\ \Leftrightarrow -6x^2-12x=0 \\ \Leftrightarrow x(-6x-12) = 0 \\ \Leftrightarrow x = 0 \vee -6x-12=0 \\ \Leftrightarrow x = 0 \vee x = \frac{12}{-6} = -2 \\ V = \Big\{ 0 ; -2 \Big\} \\ -----------------\)
12. \(5x^2+5x=10x^2-9x \\ \Leftrightarrow -5x^2+14x=0 \\ \Leftrightarrow x(-5x+14) = 0 \\ \Leftrightarrow x = 0 \vee -5x+14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-14}{-5} = \frac{14}{5} \\ V = \Big\{ \frac{14}{5}; 0 \Big\} \\ -----------------\)