Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-5x^2-845=0\)
2. \(2x^2-162=0\)
3. \(12x^2-579=9x^2+9\)
4. \(-2(-7x^2-10)=-(-18x^2+380)\)
5. \(-14x^2-390=-6x^2+2\)
6. \(-5(8x^2-2)=-(41x^2-14)\)
7. \(4(-2x^2+10)=-(15x^2-152)\)
8. \(-5(4x^2+6)=-(18x^2+32)\)
9. \(-3x^2-156=-9x^2-6\)
10. \(-6x^2+0=0\)
11. \(-5x^2+605=0\)
12. \(-5(-9x^2+6)=-(-38x^2-313)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-5x^2-845=0 \\ \Leftrightarrow -5x^2 = 845 \\ \Leftrightarrow x^2 = \frac{845}{-5} < 0 \\ V = \varnothing \\ -----------------\)
2. \(2x^2-162=0 \\ \Leftrightarrow 2x^2 = 162 \\ \Leftrightarrow x^2 = \frac{162}{2}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
3. \(12x^2-579=9x^2+9 \\ \Leftrightarrow 12x^2-9x^2=9+579 \\ \Leftrightarrow 3x^2 = 588 \\ \Leftrightarrow x^2 = \frac{588}{3}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
4. \(-2(-7x^2-10)=-(-18x^2+380) \\ \Leftrightarrow 14x^2+20=18x^2-380 \\ \Leftrightarrow 14x^2-18x^2=-380-20 \\ \Leftrightarrow -4x^2 = -400 \\ \Leftrightarrow x^2 = \frac{-400}{-4}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
5. \(-14x^2-390=-6x^2+2 \\ \Leftrightarrow -14x^2+6x^2=2+390 \\ \Leftrightarrow -8x^2 = 392 \\ \Leftrightarrow x^2 = \frac{392}{-8} < 0 \\ V = \varnothing \\ -----------------\)
6. \(-5(8x^2-2)=-(41x^2-14) \\ \Leftrightarrow -40x^2+10=-41x^2+14 \\ \Leftrightarrow -40x^2+41x^2=14-10 \\ \Leftrightarrow x^2 = 4 \\ \Leftrightarrow x^2 = \frac{4}{1}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
7. \(4(-2x^2+10)=-(15x^2-152) \\ \Leftrightarrow -8x^2+40=-15x^2+152 \\ \Leftrightarrow -8x^2+15x^2=152-40 \\ \Leftrightarrow 7x^2 = 112 \\ \Leftrightarrow x^2 = \frac{112}{7}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
8. \(-5(4x^2+6)=-(18x^2+32) \\ \Leftrightarrow -20x^2-30=-18x^2-32 \\ \Leftrightarrow -20x^2+18x^2=-32+30 \\ \Leftrightarrow -2x^2 = -2 \\ \Leftrightarrow x^2 = \frac{-2}{-2}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
9. \(-3x^2-156=-9x^2-6 \\ \Leftrightarrow -3x^2+9x^2=-6+156 \\ \Leftrightarrow 6x^2 = 150 \\ \Leftrightarrow x^2 = \frac{150}{6}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
10. \(-6x^2+0=0 \\ \Leftrightarrow -6x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-6}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
11. \(-5x^2+605=0 \\ \Leftrightarrow -5x^2 = -605 \\ \Leftrightarrow x^2 = \frac{-605}{-5}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
12. \(-5(-9x^2+6)=-(-38x^2-313) \\ \Leftrightarrow 45x^2-30=38x^2+313 \\ \Leftrightarrow 45x^2-38x^2=313+30 \\ \Leftrightarrow 7x^2 = 343 \\ \Leftrightarrow x^2 = \frac{343}{7}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)