Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-6x^2+1350=0\)
2. \(x^2-25=0\)
3. \(5(4x^2-9)=-(-23x^2+345)\)
4. \(-8x^2-392=0\)
5. \(-13x^2+1193=-6x^2+10\)
6. \(3(10x^2-4)=-(-22x^2+404)\)
7. \(-3(4x^2+2)=-(6x^2-48)\)
8. \(4x^2-35=7x^2-8\)
9. \(-2(8x^2-5)=-(18x^2-172)\)
10. \(-2x^2+32=0\)
11. \(-6x^2+1176=0\)
12. \(-2x^2-32=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-6x^2+1350=0 \\ \Leftrightarrow -6x^2 = -1350 \\ \Leftrightarrow x^2 = \frac{-1350}{-6}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
2. \(x^2-25=0 \\ \Leftrightarrow x^2 = 25 \\ \Leftrightarrow x^2 = \frac{25}{1}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
3. \(5(4x^2-9)=-(-23x^2+345) \\ \Leftrightarrow 20x^2-45=23x^2-345 \\ \Leftrightarrow 20x^2-23x^2=-345+45 \\ \Leftrightarrow -3x^2 = -300 \\ \Leftrightarrow x^2 = \frac{-300}{-3}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
4. \(-8x^2-392=0 \\ \Leftrightarrow -8x^2 = 392 \\ \Leftrightarrow x^2 = \frac{392}{-8} < 0 \\ V = \varnothing \\ -----------------\)
5. \(-13x^2+1193=-6x^2+10 \\ \Leftrightarrow -13x^2+6x^2=10-1193 \\ \Leftrightarrow -7x^2 = -1183 \\ \Leftrightarrow x^2 = \frac{-1183}{-7}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
6. \(3(10x^2-4)=-(-22x^2+404) \\ \Leftrightarrow 30x^2-12=22x^2-404 \\ \Leftrightarrow 30x^2-22x^2=-404+12 \\ \Leftrightarrow 8x^2 = -392 \\ \Leftrightarrow x^2 = \frac{-392}{8} < 0 \\ V = \varnothing \\ -----------------\)
7. \(-3(4x^2+2)=-(6x^2-48) \\ \Leftrightarrow -12x^2-6=-6x^2+48 \\ \Leftrightarrow -12x^2+6x^2=48+6 \\ \Leftrightarrow -6x^2 = 54 \\ \Leftrightarrow x^2 = \frac{54}{-6} < 0 \\ V = \varnothing \\ -----------------\)
8. \(4x^2-35=7x^2-8 \\ \Leftrightarrow 4x^2-7x^2=-8+35 \\ \Leftrightarrow -3x^2 = 27 \\ \Leftrightarrow x^2 = \frac{27}{-3} < 0 \\ V = \varnothing \\ -----------------\)
9. \(-2(8x^2-5)=-(18x^2-172) \\ \Leftrightarrow -16x^2+10=-18x^2+172 \\ \Leftrightarrow -16x^2+18x^2=172-10 \\ \Leftrightarrow 2x^2 = 162 \\ \Leftrightarrow x^2 = \frac{162}{2}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
10. \(-2x^2+32=0 \\ \Leftrightarrow -2x^2 = -32 \\ \Leftrightarrow x^2 = \frac{-32}{-2}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
11. \(-6x^2+1176=0 \\ \Leftrightarrow -6x^2 = -1176 \\ \Leftrightarrow x^2 = \frac{-1176}{-6}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
12. \(-2x^2-32=0 \\ \Leftrightarrow -2x^2 = 32 \\ \Leftrightarrow x^2 = \frac{32}{-2} < 0 \\ V = \varnothing \\ -----------------\)