Question

First factor the trinomial as a binomial square and then use the square root method to solve. Round the solution to the nearest tenth. x2 - 14x + 49 = 3

Answer 1

\[x=7+\sqrt{3}\]

Answer 2

and x=7-sqrt(3)

x=8.7 & 5,3

Answer 3

49 is a perfect square (7 squared), 1 (leading coefficient)
so, this is a perfect square in the form (a^2 + 2ab + b^2, where b^2 = 49,so b=7 or b=-7 (it would be -7 because middle term is negative) and a=1x

(x-7)^2 = 3 take square root of both sides
|x-7| = sqrt(3) (absolute values because x-7 can either be positive or negative before squaring it

x-7 = +- sqrt(3)
x = 7 +- sqrt(3)
x = 7 + sqrt(3) and 7 - sqrt(3) ; then you can approximate answer