Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-14x^2-37=-9x^2+8\)
2. \(6x^2+789=10x^2+5\)
3. \(8x^2-648=0\)
4. \(-3(8x^2-8)=-(23x^2+12)\)
5. \(5x^2+845=0\)
6. \(-x^2-49=0\)
7. \(-4(6x^2-5)=-(16x^2-220)\)
8. \(-5x^2-500=0\)
9. \(4(6x^2+5)=-(-19x^2+700)\)
10. \(-6x^2-14=-9x^2-2\)
11. \(5x^2-5=0\)
12. \(5(4x^2-3)=-(-17x^2-228)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-14x^2-37=-9x^2+8 \\ \Leftrightarrow -14x^2+9x^2=8+37 \\ \Leftrightarrow -5x^2 = 45 \\ \Leftrightarrow x^2 = \frac{45}{-5} < 0 \\ V = \varnothing \\ -----------------\)
2. \(6x^2+789=10x^2+5 \\ \Leftrightarrow 6x^2-10x^2=5-789 \\ \Leftrightarrow -4x^2 = -784 \\ \Leftrightarrow x^2 = \frac{-784}{-4}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
3. \(8x^2-648=0 \\ \Leftrightarrow 8x^2 = 648 \\ \Leftrightarrow x^2 = \frac{648}{8}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
4. \(-3(8x^2-8)=-(23x^2+12) \\ \Leftrightarrow -24x^2+24=-23x^2-12 \\ \Leftrightarrow -24x^2+23x^2=-12-24 \\ \Leftrightarrow -x^2 = -36 \\ \Leftrightarrow x^2 = \frac{-36}{-1}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
5. \(5x^2+845=0 \\ \Leftrightarrow 5x^2 = -845 \\ \Leftrightarrow x^2 = \frac{-845}{5} < 0 \\ V = \varnothing \\ -----------------\)
6. \(-x^2-49=0 \\ \Leftrightarrow -x^2 = 49 \\ \Leftrightarrow x^2 = \frac{49}{-1} < 0 \\ V = \varnothing \\ -----------------\)
7. \(-4(6x^2-5)=-(16x^2-220) \\ \Leftrightarrow -24x^2+20=-16x^2+220 \\ \Leftrightarrow -24x^2+16x^2=220-20 \\ \Leftrightarrow -8x^2 = 200 \\ \Leftrightarrow x^2 = \frac{200}{-8} < 0 \\ V = \varnothing \\ -----------------\)
8. \(-5x^2-500=0 \\ \Leftrightarrow -5x^2 = 500 \\ \Leftrightarrow x^2 = \frac{500}{-5} < 0 \\ V = \varnothing \\ -----------------\)
9. \(4(6x^2+5)=-(-19x^2+700) \\ \Leftrightarrow 24x^2+20=19x^2-700 \\ \Leftrightarrow 24x^2-19x^2=-700-20 \\ \Leftrightarrow 5x^2 = -720 \\ \Leftrightarrow x^2 = \frac{-720}{5} < 0 \\ V = \varnothing \\ -----------------\)
10. \(-6x^2-14=-9x^2-2 \\ \Leftrightarrow -6x^2+9x^2=-2+14 \\ \Leftrightarrow 3x^2 = 12 \\ \Leftrightarrow x^2 = \frac{12}{3}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
11. \(5x^2-5=0 \\ \Leftrightarrow 5x^2 = 5 \\ \Leftrightarrow x^2 = \frac{5}{5}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
12. \(5(4x^2-3)=-(-17x^2-228) \\ \Leftrightarrow 20x^2-15=17x^2+228 \\ \Leftrightarrow 20x^2-17x^2=228+15 \\ \Leftrightarrow 3x^2 = 243 \\ \Leftrightarrow x^2 = \frac{243}{3}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)