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

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

How do you solve 15 + 26d = -8d²15 + 26d = -8d²?