How do you solve #d^2+56=-18d#?

1 Answer
Mar 31, 2017

Answer:

First, we put it into the ‘standard’ quadratic formula form. Then we factor it into roots.

Explanation:

#d^2 + 56 = −18d# ; #d^2 + 18d + 56 = 0#
#(d + ?)*(d + ??) = 0# We need to find the constants that add up to 18 and multiply to 56.
Even multiples of 56 are 2 and 4. Only 4 works with 14 to give us both the multiple (4*14) and the sum (4 + 14) that we need to satisfy the equation.
#(d + 4)*(d + 14) = 0#
So our solutions (roots) are: d = -4 and d = -14.

CHECK:
#-4^2 + 18*(-4) + 56 = 0# ; 16 – 72 *56 = 0 ; 0 = 0 CORRECT.