Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(5(3x^2+9x)=-(-8x^2-46x)\)
2. \(4(-8x^2-5x)=-(39x^2+32x)\)
3. \(-5x^2+10x=-2x^2-7x\)
4. \(-2(-8x^2+8x)=-(-14x^2+18x)\)
5. \(-7x^2-6x=0\)
6. \(x^2+9x=0\)
7. \(-13x^2-11x=-7x^2-6x\)
8. \(7x^2-10x=0\)
9. \(5(-2x^2-7x)=-(17x^2+52x)\)
10. \(3(9x^2+6x)=-(-30x^2-38x)\)
11. \(11x^2+31x=5x^2+7x\)
12. \(-4(9x^2+2x)=-(31x^2-2x)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(5(3x^2+9x)=-(-8x^2-46x) \\ \Leftrightarrow 15x^2+45x=8x^2+46x \\ \Leftrightarrow 15x^2+45x-8x^2-46x= 0 \\ \Leftrightarrow 7x^2+1x=0 \\ \Leftrightarrow x(7x+1) = 0 \\ \Leftrightarrow x = 0 \vee 7x+1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-1}{7} \\ V = \Big\{ 0 ; \frac{-1}{7} \Big\} \\ -----------------\)
2. \(4(-8x^2-5x)=-(39x^2+32x) \\ \Leftrightarrow -32x^2-20x=-39x^2-32x \\ \Leftrightarrow -32x^2-20x+39x^2+32x= 0 \\ \Leftrightarrow 7x^2-12x=0 \\ \Leftrightarrow x(7x-12) = 0 \\ \Leftrightarrow x = 0 \vee 7x-12=0 \\ \Leftrightarrow x = 0 \vee x = \frac{12}{7} \\ V = \Big\{ \frac{12}{7}; 0 \Big\} \\ -----------------\)
3. \(-5x^2+10x=-2x^2-7x \\ \Leftrightarrow -3x^2+17x=0 \\ \Leftrightarrow x(-3x+17) = 0 \\ \Leftrightarrow x = 0 \vee -3x+17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-17}{-3} = \frac{17}{3} \\ V = \Big\{ \frac{17}{3}; 0 \Big\} \\ -----------------\)
4. \(-2(-8x^2+8x)=-(-14x^2+18x) \\ \Leftrightarrow 16x^2-16x=14x^2-18x \\ \Leftrightarrow 16x^2-16x-14x^2+18x= 0 \\ \Leftrightarrow 2x^2-2x=0 \\ \Leftrightarrow x(2x-2) = 0 \\ \Leftrightarrow x = 0 \vee 2x-2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{2}{2} = 1 \\ V = \Big\{ 1; 0 \Big\} \\ -----------------\)
5. \(-7x^2-6x=0 \\ \Leftrightarrow x(-7x-6) = 0 \\ \Leftrightarrow x = 0 \vee -7x-6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{6}{-7} = \frac{-6}{7} \\ V = \Big\{ 0 ; \frac{-6}{7} \Big\} \\ -----------------\)
6. \(x^2+9x=0 \\ \Leftrightarrow x(x+9) = 0 \\ \Leftrightarrow x = 0 \vee x+9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-9}{1} = -9 \\ V = \Big\{ 0 ; -9 \Big\} \\ -----------------\)
7. \(-13x^2-11x=-7x^2-6x \\ \Leftrightarrow -6x^2-5x=0 \\ \Leftrightarrow x(-6x-5) = 0 \\ \Leftrightarrow x = 0 \vee -6x-5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{5}{-6} = \frac{-5}{6} \\ V = \Big\{ 0 ; \frac{-5}{6} \Big\} \\ -----------------\)
8. \(7x^2-10x=0 \\ \Leftrightarrow x(7x-10) = 0 \\ \Leftrightarrow x = 0 \vee 7x-10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{10}{7} \\ V = \Big\{ \frac{10}{7}; 0 \Big\} \\ -----------------\)
9. \(5(-2x^2-7x)=-(17x^2+52x) \\ \Leftrightarrow -10x^2-35x=-17x^2-52x \\ \Leftrightarrow -10x^2-35x+17x^2+52x= 0 \\ \Leftrightarrow 7x^2-17x=0 \\ \Leftrightarrow x(7x-17) = 0 \\ \Leftrightarrow x = 0 \vee 7x-17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{17}{7} \\ V = \Big\{ \frac{17}{7}; 0 \Big\} \\ -----------------\)
10. \(3(9x^2+6x)=-(-30x^2-38x) \\ \Leftrightarrow 27x^2+18x=30x^2+38x \\ \Leftrightarrow 27x^2+18x-30x^2-38x= 0 \\ \Leftrightarrow -3x^2+20x=0 \\ \Leftrightarrow x(-3x+20) = 0 \\ \Leftrightarrow x = 0 \vee -3x+20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-20}{-3} = \frac{20}{3} \\ V = \Big\{ \frac{20}{3}; 0 \Big\} \\ -----------------\)
11. \(11x^2+31x=5x^2+7x \\ \Leftrightarrow 6x^2+24x=0 \\ \Leftrightarrow x(6x+24) = 0 \\ \Leftrightarrow x = 0 \vee 6x+24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-24}{6} = -4 \\ V = \Big\{ 0 ; -4 \Big\} \\ -----------------\)
12. \(-4(9x^2+2x)=-(31x^2-2x) \\ \Leftrightarrow -36x^2-8x=-31x^2+2x \\ \Leftrightarrow -36x^2-8x+31x^2-2x= 0 \\ \Leftrightarrow -5x^2+10x=0 \\ \Leftrightarrow x(-5x+10) = 0 \\ \Leftrightarrow x = 0 \vee -5x+10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-10}{-5} = 2 \\ V = \Big\{ 2; 0 \Big\} \\ -----------------\)