Odgovor:
a) # 2 (x + 2) ^ 2-3 #
b) # 10 (x-2) ^ 2 #
Obrazloženje:
a) # 2x ^ 2 + 16x + 5 #
# => 2 x ^ 2 + 8 x + 5/2 #
# (Boja (crvena) a + boja (plava) b) ^ 2-a ^ 2 + boje (zeleno) 2color (crveno) acolor (plavo) b + b ^ 2 #
# => 2 boja (crvena) x ^ 2 + boje (zeleno) 2 * boja (plava) 4color (crveno) x + boje (plava) 4 ^ 2 ^ 2-4 + 5/2 #
# => 2 (boja (crvena) x ^ 2 + boje (zeleno) 2 * boja (plava) 4color (crveno) x + boje (plava) 4 ^ 2) -16 + 5/2 #
# => 2 (x + 4) ^ 2-32 / 2 + 5/2 #
# => 2 (x + 4) ^ 2-27 / 2 #
# => 2 (x + 4) ^ 2-cancel2 * 27 / cancel2 #
# => 2 (x + 4) ^ 2-27 #
b) # 6 + 4x-x ^ 2 #
# => - 1 * x ^ 2-4 *-6 #
# => - 1 * boja (crvena) x ^ 2color (zeleno) 2 * boja (plava) 2color (crveno) x + boje (plava) 2 ^ 2-2 ^ 2-6 #
# => - 1 * (boja (crvena) x ^ 2color (zeleno) 2 * boja (plava) 2color (crveno) x + boje (plava) 2 ^ 2) -4-6 #
# => - 1 * (boja (crvena) x-boje (plava) 2) ^ 2-10 #
# => - (x-2) ^ 2 + 10 #
# => 10 (x-2) ^ 2 #
Uz pretpostavku da ćemo riješiti jednadžbe koje završavaju kvadratnom metodom.
a) # 2x ^ 2 + 16x + 5 = 0 #
# => X ^ 2 + 8 x + 5/2 = 0 #
# => X ^ 2 * 2 + x * 4 + 4 ^ 2-4 ^ 2 + 5/2 = 0 #
# => (X + 4) ^ 2-16 + 5/2 = 0 #
# => (X + 4) ^ 2-27 / 2 = 0 #
# => (X + 4) ^ 2 = 27/2 #
# => X = + 4 pmsqrt27 / 2 #
# => X = -4pm (3sqrt3) / 2 #
(B) # 6 + 4x-x ^ 2 = 0 #
# => 6 + 2 ^ 2-2 ^ 2 + 2 * X * 2 x ^ 2 = 0 #
# => 10- (2 ^ 2-2 * * x 2 + x ^ 2) = 0 #
# => (x-2) ^ 2 = 10 #
# => x-2 = pmsqrt10 #
# => X = 2pmsqrt10 #
