How do you solve #5x^2-10x=7x^2+17# using any method?

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Answer 1 · 2017-02-03T10:20:58

#x = -5/2 - i3/2#, #x = -5/2 -i3/2#

#"Solve with quadratic formula"#

#5x^2 - 10x = 7x^2 + 17 #

#"Subtract 7x^2 + 17 from both sides"#

#5x^2 - 10x - (7x^2 + 17) = 7x^2 + 17 - (7x^2 + 17)#

#"Refine"#

#-2x^2 - 10x - 17 = 0#

#"Quadratic Equation Formula"#

#x_1,2 = {-b± sqrt (b^2 - 4"ac")}/"2a"#

#a = -2, b = -10, c = -17: #

#x_1,2 = {-(-10) ± sqrt (-10^2 - 4(-2)(-17))}/"2(-2)"#

#x_1,2 = {-(-10) + sqrt (-10^2 - 4(-2)(-17))}/"2(-2)" = -5/2 - i3/2#

#x_1,2 = {-(-10) - sqrt (-10^2 - 4(-2)(-17))}/"2(-2)"= -5/2 + i3/2#

#x = -5/2 - i3/2#, #x = -5/2 -i3/2#