Express 8x² + 10x - 5 in the form a(x + b)² + c. Hence, solve the quadratic equation 8x² + 10x - 5 = 0, giving the answers correct to two decimal places?

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Answer 1 · 2018-05-22T12:50:04

#8 x^2+10 x-5 = 8(x+5/8)^2-65/8 #
Solution: #x ~~ -1.63 and x ~~ 0.38 #

#8 x^2+10 x-5 = 8 (x^2+5/4 x)-5 #

#= 8 {x^2+5/4 x +(5/8)^2}-8*(5/8)^2-5 #

#=8(x+5/8)^2-25/8-5 #

#=8(x+5/8)^2-65/8 #

#:.8 x^2+10 x-5 = 8(x+5/8)^2-8.125 #

#8(x+5/8)^2-65/8 = 0 # or

#8(x+5/8)^2 =65/8 # or

#(x+5/8)^2 = 65/64 # or

#(x+5/8) = +- sqrt (65/64) # or

#x = -5/8 +- sqrt 65/8#

#:. x ~~ -1.63 and x ~~ 0.38 # [Ans]