Question

what is x if the problem is: (x+2)(x+4)=30+x

Answer 1

(x+2)(x+4) = 30 + x
first we expand the left side of the equation,, multiplying them,
x^2 + 2x + 4x + 8 = 30 + x
then we combine similar terms and make the right side of equation equal to zero (since it's quadratic equation) :
x^2 + 6x + 8 - 30 - x = 0
x^2 + 5x - 22 = 0
now, since it's not factorable, we use quadratic formula
x = [-b +- sqrt(b^2 - 4ac)]/(2a)
note: +- is plus or minus
substituting,
x = [-5 +- sqrt(5^2 - 4(1)(-22))]/(2*1)
x = [-5 +- sqrt(25 +88)]/2
x = [-5 +- sqrt(113)]/2
separating this into plus and minus:
x = [-5 + sqrt(113)]/2 ; and
x = [-5 - sqrt(113)]/2

hope this helps~ :)