How do you solve #15 + 26d = -8d²#?

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Answer 1 · 2018-03-31T12:35:57

#d_1=-3/4 or d_2=-5/2#

First, bring everything to one side.

#15 + 26d = -8d^2|+8d^2#
#8d^2+26d+15=0#

Divide by the coefficient of #d^2# which is #8#

#8d^2+26d+15=0|:8#
#d^2+13/4d+15/8=0#

Complete the square (#a^2+2ab+b^2=(a+b)^2#)

#d^2+13/4dcolor(blue)(+(13/8)^2-(13/8)^2)+15/8=0#
#(d+13/8)^2-(13/8)^2+15/8=(d+13/8)^2-49/64=0#

Solve for d

#0=(d+13/8)^2-49/64|+49/64|sqrt()|-13/8#
#+-sqrt(49/64)-13/8=d#
#+-7/8-13/8=d#
#d_1=-3/4 or d_2=-5/2#