#(5s + 7) ( s + 5) = 23#
Use BODMAS rule.
First solve brackets using distributive property:
#5s (s +5) + 7( s + 5) = 23#
# 5s^2 + 25 +7s + 35 =23#
# 5s^2 +7s + 60 =23#
# 5s^2 +7s + 60 -23= 0#
# 5s^2 +7s + 60 -23= 0#
# 5s^2 +7s + 37= 0#
According to the Quadratic Formula, s , the solution for #as^2+bs+c = 0# , where a, b and c are coefficients, is given by :
#s = - b ± sqrt( b2-4ac)/(2a)#
In our case, # a = 5#
# b = 7#
#c = 37 #
Accordingly, #(b^2 - 4ac) = 49 - 740#
#= -691#
Applying the quadratic formula :
#s = -7 ± sqrt( -691 )/10#
#i # and # -i # are the square roots of minus 1
Accordingly,
#sqrt( -691) = sqrt (691\times(-1)) #
# = sqrt (691 )\times sqrt( -1) =
± sqrt (691) i #
#sqrt(691)# when rounded to 4 decimal digits, =# 26.2869#
Now,
# s = ( -7 ± 26.287 i ) / 10#
We have two imaginary solutions :
#s =(-7+sqrt(-691))/10=(-7+isqrt(691) )/10= -0.7000+2.6287i#
or:
#s =(-7-sqrt(-691))/10=(-7-isqrt(691) )/10= -0.7000-2.6287i#
