Question

solve by completing the square.x squared -9x=-14. please show work :)

Answer 1

x^2 - 9x = -14
x^2 - 9x + (9/2)^2 = -14 + (9/2)^2
x^2 -9x + 81/4 = -14 + 81/4
(x-9/2)^2 = 81/4 - 56/4
(x-9/2)^2 = 25/4
x - 9/2 = sqrt (25/4)
x - 9/2 = +/- 5/2
x = 9/2 +/- 5/2
x = 14/2; x = 4/2
x=7
x = 2

Answer 2

take half of 2nd term and square it
(-9/2)^2 = 81/4
add this to both sides

--> x^2 -9x + 81/4 = -14 +81/4
the left side can now be factored into perfect square
--> (x-9/2)^2 = 25/4

take square root
--> x-9/2 = +-5/2
--> x = 9/2 +- 5/2
--> x = 7 or 2