Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-2x^2+319=-6x^2-5\)
2. \(-2x^2-92=-3x^2+8\)
3. \(-x^2+36=0\)
4. \(-5x^2-1570=3x^2-2\)
5. \(6x^2-1014=0\)
6. \(-5(-9x^2-9)=-(-50x^2-170)\)
7. \(-4(-7x^2-5)=-(-30x^2+78)\)
8. \(15x^2-49=9x^2+5\)
9. \(-5(-8x^2+8)=-(-39x^2-41)\)
10. \(-2(-2x^2+7)=-(-x^2-493)\)
11. \(-6x^2-150=0\)
12. \(2(-9x^2-3)=-(13x^2+11)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-2x^2+319=-6x^2-5 \\ \Leftrightarrow -2x^2+6x^2=-5-319 \\ \Leftrightarrow 4x^2 = -324 \\ \Leftrightarrow x^2 = \frac{-324}{4} < 0 \\ V = \varnothing \\ -----------------\)
2. \(-2x^2-92=-3x^2+8 \\ \Leftrightarrow -2x^2+3x^2=8+92 \\ \Leftrightarrow x^2 = 100 \\ \Leftrightarrow x^2 = \frac{100}{1}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
3. \(-x^2+36=0 \\ \Leftrightarrow -x^2 = -36 \\ \Leftrightarrow x^2 = \frac{-36}{-1}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
4. \(-5x^2-1570=3x^2-2 \\ \Leftrightarrow -5x^2-3x^2=-2+1570 \\ \Leftrightarrow -8x^2 = 1568 \\ \Leftrightarrow x^2 = \frac{1568}{-8} < 0 \\ V = \varnothing \\ -----------------\)
5. \(6x^2-1014=0 \\ \Leftrightarrow 6x^2 = 1014 \\ \Leftrightarrow x^2 = \frac{1014}{6}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
6. \(-5(-9x^2-9)=-(-50x^2-170) \\ \Leftrightarrow 45x^2+45=50x^2+170 \\ \Leftrightarrow 45x^2-50x^2=170-45 \\ \Leftrightarrow -5x^2 = 125 \\ \Leftrightarrow x^2 = \frac{125}{-5} < 0 \\ V = \varnothing \\ -----------------\)
7. \(-4(-7x^2-5)=-(-30x^2+78) \\ \Leftrightarrow 28x^2+20=30x^2-78 \\ \Leftrightarrow 28x^2-30x^2=-78-20 \\ \Leftrightarrow -2x^2 = -98 \\ \Leftrightarrow x^2 = \frac{-98}{-2}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
8. \(15x^2-49=9x^2+5 \\ \Leftrightarrow 15x^2-9x^2=5+49 \\ \Leftrightarrow 6x^2 = 54 \\ \Leftrightarrow x^2 = \frac{54}{6}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
9. \(-5(-8x^2+8)=-(-39x^2-41) \\ \Leftrightarrow 40x^2-40=39x^2+41 \\ \Leftrightarrow 40x^2-39x^2=41+40 \\ \Leftrightarrow x^2 = 81 \\ \Leftrightarrow x^2 = \frac{81}{1}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
10. \(-2(-2x^2+7)=-(-x^2-493) \\ \Leftrightarrow 4x^2-14=x^2+493 \\ \Leftrightarrow 4x^2-x^2=493+14 \\ \Leftrightarrow 3x^2 = 507 \\ \Leftrightarrow x^2 = \frac{507}{3}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
11. \(-6x^2-150=0 \\ \Leftrightarrow -6x^2 = 150 \\ \Leftrightarrow x^2 = \frac{150}{-6} < 0 \\ V = \varnothing \\ -----------------\)
12. \(2(-9x^2-3)=-(13x^2+11) \\ \Leftrightarrow -18x^2-6=-13x^2-11 \\ \Leftrightarrow -18x^2+13x^2=-11+6 \\ \Leftrightarrow -5x^2 = -5 \\ \Leftrightarrow x^2 = \frac{-5}{-5}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)