Question

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

Answer 1

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.