Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(7x^2+5x=6x^2-4x\)
2. \(2(10x^2+6x)=-(-12x^2+3x)\)
3. \(-6x^2-2x=-10x^2-9x\)
4. \(-3(-7x^2+6x)=-(-17x^2+40x)\)
5. \(8x^2+15x=0\)
6. \(5(6x^2+3x)=-(-28x^2-23x)\)
7. \(-11x^2+2x=-4x^2-8x\)
8. \(2(-10x^2-3x)=-(28x^2+0x)\)
9. \(-5x^2-20x=0\)
10. \(-6x^2+7x=0\)
11. \(-3x^2-13x=-8x^2-5x\)
12. \(2(10x^2+10x)=-(-28x^2-22x)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(7x^2+5x=6x^2-4x \\ \Leftrightarrow x^2+9x=0 \\ \Leftrightarrow x(x+9) = 0 \\ \Leftrightarrow x = 0 \vee x+9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-9}{1} = -9 \\ V = \Big\{ 0 ; -9 \Big\} \\ -----------------\)
2. \(2(10x^2+6x)=-(-12x^2+3x) \\ \Leftrightarrow 20x^2+12x=12x^2-3x \\ \Leftrightarrow 20x^2+12x-12x^2+3x= 0 \\ \Leftrightarrow 8x^2-15x=0 \\ \Leftrightarrow x(8x-15) = 0 \\ \Leftrightarrow x = 0 \vee 8x-15=0 \\ \Leftrightarrow x = 0 \vee x = \frac{15}{8} \\ V = \Big\{ \frac{15}{8}; 0 \Big\} \\ -----------------\)
3. \(-6x^2-2x=-10x^2-9x \\ \Leftrightarrow 4x^2+7x=0 \\ \Leftrightarrow x(4x+7) = 0 \\ \Leftrightarrow x = 0 \vee 4x+7=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-7}{4} \\ V = \Big\{ 0 ; \frac{-7}{4} \Big\} \\ -----------------\)
4. \(-3(-7x^2+6x)=-(-17x^2+40x) \\ \Leftrightarrow 21x^2-18x=17x^2-40x \\ \Leftrightarrow 21x^2-18x-17x^2+40x= 0 \\ \Leftrightarrow 4x^2-22x=0 \\ \Leftrightarrow x(4x-22) = 0 \\ \Leftrightarrow x = 0 \vee 4x-22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{22}{4} = \frac{11}{2} \\ V = \Big\{ \frac{11}{2}; 0 \Big\} \\ -----------------\)
5. \(8x^2+15x=0 \\ \Leftrightarrow x(8x+15) = 0 \\ \Leftrightarrow x = 0 \vee 8x+15=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-15}{8} \\ V = \Big\{ 0 ; \frac{-15}{8} \Big\} \\ -----------------\)
6. \(5(6x^2+3x)=-(-28x^2-23x) \\ \Leftrightarrow 30x^2+15x=28x^2+23x \\ \Leftrightarrow 30x^2+15x-28x^2-23x= 0 \\ \Leftrightarrow 2x^2+8x=0 \\ \Leftrightarrow x(2x+8) = 0 \\ \Leftrightarrow x = 0 \vee 2x+8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-8}{2} = -4 \\ V = \Big\{ 0 ; -4 \Big\} \\ -----------------\)
7. \(-11x^2+2x=-4x^2-8x \\ \Leftrightarrow -7x^2+10x=0 \\ \Leftrightarrow x(-7x+10) = 0 \\ \Leftrightarrow x = 0 \vee -7x+10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-10}{-7} = \frac{10}{7} \\ V = \Big\{ \frac{10}{7}; 0 \Big\} \\ -----------------\)
8. \(2(-10x^2-3x)=-(28x^2+0x) \\ \Leftrightarrow -20x^2-6x=-28x^2+0x \\ \Leftrightarrow -20x^2-6x+28x^2+0x= 0 \\ \Leftrightarrow 8x^2+6x=0 \\ \Leftrightarrow x(8x+6) = 0 \\ \Leftrightarrow x = 0 \vee 8x+6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-6}{8} = \frac{-3}{4} \\ V = \Big\{ 0 ; \frac{-3}{4} \Big\} \\ -----------------\)
9. \(-5x^2-20x=0 \\ \Leftrightarrow x(-5x-20) = 0 \\ \Leftrightarrow x = 0 \vee -5x-20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{20}{-5} = -4 \\ V = \Big\{ 0 ; -4 \Big\} \\ -----------------\)
10. \(-6x^2+7x=0 \\ \Leftrightarrow x(-6x+7) = 0 \\ \Leftrightarrow x = 0 \vee -6x+7=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-7}{-6} = \frac{7}{6} \\ V = \Big\{ \frac{7}{6}; 0 \Big\} \\ -----------------\)
11. \(-3x^2-13x=-8x^2-5x \\ \Leftrightarrow 5x^2-8x=0 \\ \Leftrightarrow x(5x-8) = 0 \\ \Leftrightarrow x = 0 \vee 5x-8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{8}{5} \\ V = \Big\{ \frac{8}{5}; 0 \Big\} \\ -----------------\)
12. \(2(10x^2+10x)=-(-28x^2-22x) \\ \Leftrightarrow 20x^2+20x=28x^2+22x \\ \Leftrightarrow 20x^2+20x-28x^2-22x= 0 \\ \Leftrightarrow -8x^2+2x=0 \\ \Leftrightarrow x(-8x+2) = 0 \\ \Leftrightarrow x = 0 \vee -8x+2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-2}{-8} = \frac{1}{4} \\ V = \Big\{ \frac{1}{4}; 0 \Big\} \\ -----------------\)