How do you solve the equation #2x^2+10x=-17# by completing the square?

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Answer 1 · 2018-03-03T10:23:13

#color(red)(x = # #color(green)(-(1/2)(5-3i), (-1/2)(5+3i)#

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

Divide by 2 on both sides. #x^2 + 5x = -17/2#

Rewrite the (xy term as multiple of 2#

#x^2 + (2 * x * (5/2)) = -17/2#

Complete the square on L H S by adding #(5/2)^2# to both sides.

#x^2 + (2*(5/2) x+ (5/2)^2 = -17 / 2 + (5/2)^2 = -9/4#

#(x+5/2)^2 = (sqrt(-9/4)^2 = (i * (3/2)^2#

#x + 5/2 = +- (3/2)i#

#color(red)(x ) = color(blue)(-5/2 + 3/2i, -5/2 -3/2i# or #color(green)(-(1/2)(5-3i), (-1/2)(5+3i)#