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

Mar 31, 2017

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

#### Explanation:

d^2 + 56 = −18d ; ${d}^{2} + 18 d + 56 = 0$
(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.
$\left(d + 4\right) \cdot \left(d + 14\right) = 0$
So our solutions (roots) are: d = -4 and d = -14.

CHECK:
$- {4}^{2} + 18 \cdot \left(- 4\right) + 56 = 0$ ; 16 – 72 *56 = 0 ; 0 = 0 CORRECT.