Question

How do you factor and solve `r^2+8r+14=0`?

Answer 1

`x = - 4 +- sqrt2`

Explanation:

Use the improved quadratic formula in graphic form (Google)
`y = r^2 + 8r + 14 = 0`
`D = d^2 = b^2 - 4ac = 64 - 56 = 8` --> `d = +- 2sqrt2`
There are 2 real roots:
`x = -b/(2a) +- d/(2a) = -8/2 +- (2sqrt2)/2 = - 4 +- sqrt2`
Factored form of y:
`y = (x - x1)(x - x2) = (x + 4 - sqrt2)(x + 4 + sqrt2)`