completing the square?

Question

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

 

step by step would be super helpful!

Answer 1

ill give you the steps first then we can go through it  --- its quick dont worry

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