How do you solve the quadratic using the quadratic formula given #8a^2+6a=-5#?

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Answer 1 · 2017-09-26T11:59:47

Solution: #x ~~ -0.375 + 0.69597i , x ~~ -0.375 - 0.69597i#

# 8a^2+6a = -5 or 8a^2+6a +5=0 # Comparing with standard

quadratic equation # ax^2+bx+c=0# we get # a=8 ;b=6 ,c=5#

Quadratic formula is # x= (-b+- sqrt(b^2-4ac))/(2a) #

Discriminant #D=b^2-4ac= -124# is negative , so it has

complex roots .

# x= (-6+- sqrt((-6)^2-4*8*5))/(2*8) =(-6+- sqrt(-124))/(2*8) #

# x= -3/8 +- (cancel2sqrt31 i)/(cancel2*8) = -3/8 +- sqrt31/8i#

# :. x = -3/8 + sqrt31/8i , -3/8 - sqrt31/8i# or Solution:

#x ~~ -0.375 + 0.69597i , x ~~ -0.375 - 0.69597i#