Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-2x^2-18=0\)
2. \(3(9x^2+3)=-(-31x^2+475)\)
3. \(4x^2+900=0\)
4. \(2(-7x^2+4)=-(18x^2+568)\)
5. \(4(-2x^2+10)=-(7x^2-40)\)
6. \(6x^2-96=0\)
7. \(-8x^2+0=0\)
8. \(2(-7x^2-7)=-(17x^2-13)\)
9. \(7x^2-1372=0\)
10. \(-5(4x^2+3)=-(14x^2+111)\)
11. \(7x^2+678=10x^2+3\)
12. \(-10x^2-5=-9x^2-9\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-2x^2-18=0 \\ \Leftrightarrow -2x^2 = 18 \\ \Leftrightarrow x^2 = \frac{18}{-2} < 0 \\ V = \varnothing \\ -----------------\)
2. \(3(9x^2+3)=-(-31x^2+475) \\ \Leftrightarrow 27x^2+9=31x^2-475 \\ \Leftrightarrow 27x^2-31x^2=-475-9 \\ \Leftrightarrow -4x^2 = -484 \\ \Leftrightarrow x^2 = \frac{-484}{-4}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
3. \(4x^2+900=0 \\ \Leftrightarrow 4x^2 = -900 \\ \Leftrightarrow x^2 = \frac{-900}{4} < 0 \\ V = \varnothing \\ -----------------\)
4. \(2(-7x^2+4)=-(18x^2+568) \\ \Leftrightarrow -14x^2+8=-18x^2-568 \\ \Leftrightarrow -14x^2+18x^2=-568-8 \\ \Leftrightarrow 4x^2 = -576 \\ \Leftrightarrow x^2 = \frac{-576}{4} < 0 \\ V = \varnothing \\ -----------------\)
5. \(4(-2x^2+10)=-(7x^2-40) \\ \Leftrightarrow -8x^2+40=-7x^2+40 \\ \Leftrightarrow -8x^2+7x^2=40-40 \\ \Leftrightarrow -x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-1}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
6. \(6x^2-96=0 \\ \Leftrightarrow 6x^2 = 96 \\ \Leftrightarrow x^2 = \frac{96}{6}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
7. \(-8x^2+0=0 \\ \Leftrightarrow -8x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-8}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
8. \(2(-7x^2-7)=-(17x^2-13) \\ \Leftrightarrow -14x^2-14=-17x^2+13 \\ \Leftrightarrow -14x^2+17x^2=13+14 \\ \Leftrightarrow 3x^2 = 27 \\ \Leftrightarrow x^2 = \frac{27}{3}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
9. \(7x^2-1372=0 \\ \Leftrightarrow 7x^2 = 1372 \\ \Leftrightarrow x^2 = \frac{1372}{7}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
10. \(-5(4x^2+3)=-(14x^2+111) \\ \Leftrightarrow -20x^2-15=-14x^2-111 \\ \Leftrightarrow -20x^2+14x^2=-111+15 \\ \Leftrightarrow -6x^2 = -96 \\ \Leftrightarrow x^2 = \frac{-96}{-6}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
11. \(7x^2+678=10x^2+3 \\ \Leftrightarrow 7x^2-10x^2=3-678 \\ \Leftrightarrow -3x^2 = -675 \\ \Leftrightarrow x^2 = \frac{-675}{-3}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
12. \(-10x^2-5=-9x^2-9 \\ \Leftrightarrow -10x^2+9x^2=-9+5 \\ \Leftrightarrow -x^2 = -4 \\ \Leftrightarrow x^2 = \frac{-4}{-1}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)