Question

How do you solve `f^ { 2} + 26f = 25` by completing the square?

Answer 1

Solution: `f ~~ 0.93 , f ~~ -26.93`

Explanation:

`f^2+26f =25 or f^2+26f +169 = 169+25` or

`(f+13)^2= 194 or (f+13)= +-sqrt194` or

`(f+13) ~~ +-13.93 :. f~~ 0.93 or f ~~ -26.93`

Solution: `f ~~ 0.93 , f ~~ -26.93` [Ans]

Answer 2

`f = +sqrt194-13 =0.928`

or

`f = -sqrt194 -13 = -26.9`

Explanation:

Note that:

`(a+b)^2 = a^2 +2ab+b^2`

`f^2 +26f + " ? " = 25+" ? "`

The last term is found from `((b)/2)^2`

`color(blue)((26/2)^2 = 13^2 =169)`

Add `169` to both sides of the equation to complete the square.

`f^2 +26f +color(blue)(169) = 25+color(blue)(169)`

The left hand side is in the form `a^2 +2ab+b^2`

`(f+13)^2 = 194`

`f+13 = +-sqrt194`

`f = +sqrt194-13 =0.928`

or

`f = -sqrt194 -13 = -26.9`