Question

Solve the equation by completing the square x^2-14x+45=0

Answer 1

X² - 14x + 45 = 0

Complete the square of (x² -14x + ??²), the (??)² will be  the missing square.

We know 14x = (2.x).(??) → then ?? = 14/2 and ?? = 7 or (??)² = 49
Then x² - 14.x  + 49 - 49 +45
(x² - 14.x  + 49) -49 + 54

(x-7)² -4 = 0

(x-7)² = 4

√(x-7)² = √4
(x-7) = + or - 2

and x = +2 +7 = 9  or x = -2 +7 =5, then the solutions are x' = 9 & x" = 5