Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(2(-2x^2-6x)=-(5x^2+28x)\)
2. \(-7x^2-9x=0\)
3. \(-13x^2-15x=-6x^2+4x\)
4. \(-7x^2-9x=-5x^2+10x\)
5. \(-4(-6x^2+7x)=-(-27x^2+28x)\)
6. \(-3(-8x^2+2x)=-(-25x^2+x)\)
7. \(-2(9x^2-6x)=-(20x^2-22x)\)
8. \(4(6x^2+2x)=-(-27x^2-17x)\)
9. \(-7x^2-12x=0\)
10. \(x^2+11x=6x^2+2x\)
11. \(13x^2+21x=10x^2+3x\)
12. \(5(5x^2+4x)=-(-29x^2-5x)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(2(-2x^2-6x)=-(5x^2+28x) \\ \Leftrightarrow -4x^2-12x=-5x^2-28x \\ \Leftrightarrow -4x^2-12x+5x^2+28x= 0 \\ \Leftrightarrow x^2-16x=0 \\ \Leftrightarrow x(x-16) = 0 \\ \Leftrightarrow x = 0 \vee x-16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{16}{1} = 16 \\ V = \Big\{ 16; 0 \Big\} \\ -----------------\)
2. \(-7x^2-9x=0 \\ \Leftrightarrow x(-7x-9) = 0 \\ \Leftrightarrow x = 0 \vee -7x-9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{9}{-7} = \frac{-9}{7} \\ V = \Big\{ 0 ; \frac{-9}{7} \Big\} \\ -----------------\)
3. \(-13x^2-15x=-6x^2+4x \\ \Leftrightarrow -7x^2-19x=0 \\ \Leftrightarrow x(-7x-19) = 0 \\ \Leftrightarrow x = 0 \vee -7x-19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{19}{-7} = \frac{-19}{7} \\ V = \Big\{ 0 ; \frac{-19}{7} \Big\} \\ -----------------\)
4. \(-7x^2-9x=-5x^2+10x \\ \Leftrightarrow -2x^2-19x=0 \\ \Leftrightarrow x(-2x-19) = 0 \\ \Leftrightarrow x = 0 \vee -2x-19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{19}{-2} = \frac{-19}{2} \\ V = \Big\{ 0 ; \frac{-19}{2} \Big\} \\ -----------------\)
5. \(-4(-6x^2+7x)=-(-27x^2+28x) \\ \Leftrightarrow 24x^2-28x=27x^2-28x \\ \Leftrightarrow 24x^2-28x-27x^2+28x= 0 \\ \Leftrightarrow -3x^2+0x=0 \\ \Leftrightarrow -3x^2=0 \\ \Leftrightarrow x^2 = \frac{0}{-3} \\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
6. \(-3(-8x^2+2x)=-(-25x^2+x) \\ \Leftrightarrow 24x^2-6x=25x^2-x \\ \Leftrightarrow 24x^2-6x-25x^2+x= 0 \\ \Leftrightarrow -x^2+5x=0 \\ \Leftrightarrow x(-x+5) = 0 \\ \Leftrightarrow x = 0 \vee -x+5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-5}{-1} = 5 \\ V = \Big\{ 5; 0 \Big\} \\ -----------------\)
7. \(-2(9x^2-6x)=-(20x^2-22x) \\ \Leftrightarrow -18x^2+12x=-20x^2+22x \\ \Leftrightarrow -18x^2+12x+20x^2-22x= 0 \\ \Leftrightarrow 2x^2+10x=0 \\ \Leftrightarrow x(2x+10) = 0 \\ \Leftrightarrow x = 0 \vee 2x+10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-10}{2} = -5 \\ V = \Big\{ 0 ; -5 \Big\} \\ -----------------\)
8. \(4(6x^2+2x)=-(-27x^2-17x) \\ \Leftrightarrow 24x^2+8x=27x^2+17x \\ \Leftrightarrow 24x^2+8x-27x^2-17x= 0 \\ \Leftrightarrow -3x^2+9x=0 \\ \Leftrightarrow x(-3x+9) = 0 \\ \Leftrightarrow x = 0 \vee -3x+9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-9}{-3} = 3 \\ V = \Big\{ 3; 0 \Big\} \\ -----------------\)
9. \(-7x^2-12x=0 \\ \Leftrightarrow x(-7x-12) = 0 \\ \Leftrightarrow x = 0 \vee -7x-12=0 \\ \Leftrightarrow x = 0 \vee x = \frac{12}{-7} = \frac{-12}{7} \\ V = \Big\{ 0 ; \frac{-12}{7} \Big\} \\ -----------------\)
10. \(x^2+11x=6x^2+2x \\ \Leftrightarrow -5x^2+9x=0 \\ \Leftrightarrow x(-5x+9) = 0 \\ \Leftrightarrow x = 0 \vee -5x+9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-9}{-5} = \frac{9}{5} \\ V = \Big\{ \frac{9}{5}; 0 \Big\} \\ -----------------\)
11. \(13x^2+21x=10x^2+3x \\ \Leftrightarrow 3x^2+18x=0 \\ \Leftrightarrow x(3x+18) = 0 \\ \Leftrightarrow x = 0 \vee 3x+18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-18}{3} = -6 \\ V = \Big\{ 0 ; -6 \Big\} \\ -----------------\)
12. \(5(5x^2+4x)=-(-29x^2-5x) \\ \Leftrightarrow 25x^2+20x=29x^2+5x \\ \Leftrightarrow 25x^2+20x-29x^2-5x= 0 \\ \Leftrightarrow -4x^2-15x=0 \\ \Leftrightarrow x(-4x-15) = 0 \\ \Leftrightarrow x = 0 \vee -4x-15=0 \\ \Leftrightarrow x = 0 \vee x = \frac{15}{-4} = \frac{-15}{4} \\ V = \Big\{ 0 ; \frac{-15}{4} \Big\} \\ -----------------\)