completing the square Solve the equation x2 14x 9 by compl

completing the square?
Solve the equation x^2 + 14x = 9 by completing the square

Solution

1) get all the x\'s on one side of the equation
2) identify the coefficient for x (not x2, the regular x)
3) cut the coefficient from step 2 in half
4) square the # from step 3
5) add it to both sides
6) you should be able to factor the trinomial
7) make it =0

so step 1 is already done for you

2) the coefficient for the regular x is 14

3) half of 14 is 7

4) 7 squared is 49

5) add 49 to both sides so its
x^2 + 14x +49 = 9 +49
x^2 + 14x +49 = 58

6) factor
x^2 + 14x +49 factors into (x+7)(x+7), since technically its the same thing times itself, make it (x+7)2

so now you have
(x+7)2 = 58

7) make it = 0, so we just have to subtract 58


(x+7)2-58 = 0