Onvolledige VKV (c=0)

Hoofdmenu Eentje per keer  🖨

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-4(2x^2+2x)=-(7x^2+3x)\)
2. \(8x^2-25x=0\)
3. \(2(8x^2-4x)=-(-15x^2-10x)\)
4. \(-12x^2+28x=-5x^2+10x\)
5. \(5(-10x^2-10x)=-(47x^2+55x)\)
6. \(3x^2+17x=7x^2+3x\)
7. \(8x^2-3x=0\)
8. \(13x^2-14x=10x^2-4x\)
9. \(2(-8x^2-10x)=-(10x^2+15x)\)
10. \(2(5x^2+7x)=-(-12x^2-12x)\)
11. \(2(4x^2-10x)=-(-3x^2+20x)\)
12. \(-6x^2-5x=-8x^2-9x\)

---

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-4(2x^2+2x)=-(7x^2+3x) \\ \Leftrightarrow -8x^2-8x=-7x^2-3x \\ \Leftrightarrow -8x^2-8x+7x^2+3x= 0 \\ \Leftrightarrow -x^2+5x=0 \\ \Leftrightarrow x(-x+5) = 0 \\ \Leftrightarrow x = 0 \vee -x+5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-5}{-1} = 5 \\ V = \Big\{ 5; 0 \Big\} \\ -----------------\)
2. \(8x^2-25x=0 \\ \Leftrightarrow x(8x-25) = 0 \\ \Leftrightarrow x = 0 \vee 8x-25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{25}{8} \\ V = \Big\{ \frac{25}{8}; 0 \Big\} \\ -----------------\)
3. \(2(8x^2-4x)=-(-15x^2-10x) \\ \Leftrightarrow 16x^2-8x=15x^2+10x \\ \Leftrightarrow 16x^2-8x-15x^2-10x= 0 \\ \Leftrightarrow x^2+18x=0 \\ \Leftrightarrow x(x+18) = 0 \\ \Leftrightarrow x = 0 \vee x+18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-18}{1} = -18 \\ V = \Big\{ 0 ; -18 \Big\} \\ -----------------\)
4. \(-12x^2+28x=-5x^2+10x \\ \Leftrightarrow -7x^2+18x=0 \\ \Leftrightarrow x(-7x+18) = 0 \\ \Leftrightarrow x = 0 \vee -7x+18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-18}{-7} = \frac{18}{7} \\ V = \Big\{ \frac{18}{7}; 0 \Big\} \\ -----------------\)
5. \(5(-10x^2-10x)=-(47x^2+55x) \\ \Leftrightarrow -50x^2-50x=-47x^2-55x \\ \Leftrightarrow -50x^2-50x+47x^2+55x= 0 \\ \Leftrightarrow -3x^2-5x=0 \\ \Leftrightarrow x(-3x-5) = 0 \\ \Leftrightarrow x = 0 \vee -3x-5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{5}{-3} = \frac{-5}{3} \\ V = \Big\{ 0 ; \frac{-5}{3} \Big\} \\ -----------------\)
6. \(3x^2+17x=7x^2+3x \\ \Leftrightarrow -4x^2+14x=0 \\ \Leftrightarrow x(-4x+14) = 0 \\ \Leftrightarrow x = 0 \vee -4x+14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-14}{-4} = \frac{7}{2} \\ V = \Big\{ \frac{7}{2}; 0 \Big\} \\ -----------------\)
7. \(8x^2-3x=0 \\ \Leftrightarrow x(8x-3) = 0 \\ \Leftrightarrow x = 0 \vee 8x-3=0 \\ \Leftrightarrow x = 0 \vee x = \frac{3}{8} \\ V = \Big\{ \frac{3}{8}; 0 \Big\} \\ -----------------\)
8. \(13x^2-14x=10x^2-4x \\ \Leftrightarrow 3x^2-10x=0 \\ \Leftrightarrow x(3x-10) = 0 \\ \Leftrightarrow x = 0 \vee 3x-10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{10}{3} \\ V = \Big\{ \frac{10}{3}; 0 \Big\} \\ -----------------\)
9. \(2(-8x^2-10x)=-(10x^2+15x) \\ \Leftrightarrow -16x^2-20x=-10x^2-15x \\ \Leftrightarrow -16x^2-20x+10x^2+15x= 0 \\ \Leftrightarrow -6x^2+5x=0 \\ \Leftrightarrow x(-6x+5) = 0 \\ \Leftrightarrow x = 0 \vee -6x+5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-5}{-6} = \frac{5}{6} \\ V = \Big\{ \frac{5}{6}; 0 \Big\} \\ -----------------\)
10. \(2(5x^2+7x)=-(-12x^2-12x) \\ \Leftrightarrow 10x^2+14x=12x^2+12x \\ \Leftrightarrow 10x^2+14x-12x^2-12x= 0 \\ \Leftrightarrow -2x^2-2x=0 \\ \Leftrightarrow x(-2x-2) = 0 \\ \Leftrightarrow x = 0 \vee -2x-2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{2}{-2} = -1 \\ V = \Big\{ 0 ; -1 \Big\} \\ -----------------\)
11. \(2(4x^2-10x)=-(-3x^2+20x) \\ \Leftrightarrow 8x^2-20x=3x^2-20x \\ \Leftrightarrow 8x^2-20x-3x^2+20x= 0 \\ \Leftrightarrow 5x^2+0x=0 \\ \Leftrightarrow 5x^2=0 \\ \Leftrightarrow x^2 = \frac{0}{5} \\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
12. \(-6x^2-5x=-8x^2-9x \\ \Leftrightarrow 2x^2+4x=0 \\ \Leftrightarrow x(2x+4) = 0 \\ \Leftrightarrow x = 0 \vee 2x+4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-4}{2} = -2 \\ V = \Big\{ 0 ; -2 \Big\} \\ -----------------\)